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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mar. Sci.</journal-id>
<journal-title>Frontiers in Marine Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mar. Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-7745</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fmars.2023.1226024</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Marine Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Generative adversarial networks with multi-scale and attention mechanisms for underwater image enhancement</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Ziyang</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2312718"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhao</surname>
<given-names>Liquan</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1980276"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Zhong</surname>
<given-names>Tie</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="author-notes" rid="fn001">
<sup>*</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1909039"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Jia</surname>
<given-names>Yanfei</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Cui</surname>
<given-names>Ying</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Key Laboratory of Modern Power System Simulation and Control &amp; Renewable Energy Technology, Ministry of Education (Northeast Electric Power University)</institution>, <addr-line>Jilin</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>College of Electrical and Information Engineering, Beihua University</institution>, <addr-line>Jilin</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Communication Network Operations Team of System Operations Department, Zhuhai Power Supply Bureau, Guangdong Power Grid Co., Ltd.</institution>, <addr-line>Zhuhai</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>Edited by: Zhaoqiang Xia, Northwestern Polytechnical University, China</p>
</fn>
<fn fn-type="edited-by">
<p>Reviewed by: Zhenghua Huang, Wuhan Institute of Technology, China; Xuebo Zhang, Northwest Normal University, China; Jose-Luis Lisani, University of the Balearic Islands, Spain</p>
</fn>
<fn fn-type="corresp" id="fn001">
<p>*Correspondence: Tie Zhong, <email xlink:href="mailto:zht@neepu.edu.cn">zht@neepu.edu.cn</email>
</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>06</day>
<month>10</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>10</volume>
<elocation-id>1226024</elocation-id>
<history>
<date date-type="received">
<day>20</day>
<month>05</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>13</day>
<month>09</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Wang, Zhao, Zhong, Jia and Cui</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Wang, Zhao, Zhong, Jia and Cui</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>The images captured underwater are usually degraded due to the effects of light absorption and scattering. Degraded underwater images exhibit color distortion, low contrast, and blurred details, which in turn reduce the accuracy of marine biological monitoring and underwater object detection. To address this issue, a generative adversarial network with multi-scale and an attention mechanism is proposed to improve the quality of underwater images. To extract more effective features within the generative network, several modules are introduced: a multi-scale dilated convolution module, a novel attention module, and a residual module. These modules are utilized to design a generative network with a U-shaped structure. The multi-scale dilated convolution module is designed to extract features at multiple scales and expand the receptive field to capture more global information. The attention module directs the network&#x2019;s focus towards important features, thereby reducing the interference from redundant feature information. To improve the discriminative power of the adversarial network, a multi-scale discriminator is designed. It has two output feature maps with different scales. Additionally, an improved loss function for the generative adversarial network is proposed. This improvement involves incorporating the total variation loss into the traditional loss function. The performance of different methods for enhancing underwater images is evaluated using the EUVP dataset and UIEB dataset. The experimental results demonstrate that the enhanced underwater images exhibit better quality and visual effects compared to other methods.</p>
</abstract>
<kwd-group>
<kwd>underwater image enhancement</kwd>
<kwd>generative adversarial network</kwd>
<kwd>image quality</kwd>
<kwd>image visual effect</kwd>
<kwd>deep learning</kwd>
</kwd-group>
<counts>
<fig-count count="8"/>
<table-count count="4"/>
<equation-count count="12"/>
<ref-count count="40"/>
<page-count count="14"/>
<word-count count="6770"/>
</counts>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-in-acceptance</meta-name>
<meta-value>Ocean Observation</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1" sec-type="intro">
<label>1</label>
<title>Introduction</title>
<p>In recent years, computer vision technology has played an important role in marine engineering fields such as ocean data collection (<xref ref-type="bibr" rid="B6">Gavrilov and Parnum, 2010</xref>; <xref ref-type="bibr" rid="B35">Zhang et&#xa0;al., 2022</xref>), deep ocean resources exploration, and ocean environmental protection (<xref ref-type="bibr" rid="B1">Bell et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B25">Townhill et&#xa0;al., 2022</xref>). The quality of underwater images directly influences the performance of computer vision technologies. However, the underwater images are usually not clear enough with color distortion, uneven illumination, and lower contrast, which are caused by forward scattering, backward scattering, and absorption of light in the water medium. Degraded underwater images directly reduce the performance of underwater object detection, underwater image segmentation, and underwater object tracking (<xref ref-type="bibr" rid="B40">Zou et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B33">Yu et&#xa0;al., 2023</xref>). Most underwater vision systems cannot guarantee satisfactory performance under poor water conditions. Therefore, it is necessary to enhance the underwater images to improve the performance of underwater computer vision.</p>
<p>The traditional methods of image enhancement are mainly based on methods such as histogram equalization (<xref ref-type="bibr" rid="B11">Huang et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B26">Ulutas and Ustubioglu, 2021</xref>), Gamma correction (<xref ref-type="bibr" rid="B12">Huang et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B8">Huang et&#xa0;al., 2018a</xref>) and Retinex-based methods (<xref ref-type="bibr" rid="B9">Huang et&#xa0;al., 2018b</xref>). Although these methods are simple, they are not fully suitable for underwater image enhancement. There are still significant distortions in underwater images enhanced by these methods. Besides, underwater image enhancement methods based on the degradation model have been proposed (<xref ref-type="bibr" rid="B2">Cui et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B21">Luo et&#xa0;al., 2022</xref>). These methods necessitate the construction of an appropriate degradation model for underwater images, followed by the restoration of the original, undegraded underwater image by simulating the degradation process. While they exhibit improved performance for certain underwater images, they lack robustness. The complexities and variations within underwater environments make constructing a suitable degradation model challenging. Additionally, adapting a static degradation model to different underwater environments has proven difficult. As a result, underwater image enhancement methods relying on degradation models often yield subpar results for images captured in diverse underwater settings.</p>
<p>With the development of deep convolutional networks, many underwater image enhancement methods based on deep learning have been proposed in the last few years (<xref ref-type="bibr" rid="B31">Yan et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B36">Zheng and Luo, 2022</xref>). They use a large number of degraded images and high-quality images to train the network model without constructing the degradation model. Therefore, it is more suitable for different underwater environments. A generative adversarial network can be seen as a special deep learning method. Compared with the conventional deep learning network, it consists of a generative network and an adversarial network. In underwater image enhancement, the generative network is used to enhance the image, and the adversarial network is used to determine whether the input high-quality image is the generated image by the generative network or the original high-quality image. The adversarial network aids the generative network in improving the performance of underwater image enhancement. Therefore, compared with the underwater image enhancement methods based on conventional deep learning networks, the methods based on generative adversarial networks have better performance. Although many generative adversarial networks have been used for underwater image enhancement and in attempts to improve the quality of underwater images(<xref ref-type="bibr" rid="B4">Estrada et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B30">Xu et&#xa0;al., 2023</xref>), the enhanced underwater images still contain much color distortion and detail loss, which affect underwater object detection. To further improve the quality of underwater images, an efficient generative adversarial network is proposed.</p>
<p>The main contributions of this paper are summarized as follows:</p>
<list list-type="bullet">
<list-item>
<p>A generative adversarial network with a U-shaped network structure is proposed for enhancing the underwater images. The network incorporates a new multi-scale dilated convolution module, a novel attention module, and a residual module. The generative adversarial network is capable of extracting more effective features at different scales. As a result, the enhanced underwater images produced by the proposed generative adversarial network preserve more details and color information.</p>
</list-item>
<list-item>
<p>A multi-scale adversarial network is also proposed to improve the discriminative power, which is helpful in improving the optimization of the generative network. It contains two judgment score matrices at different scales to determine whether the input image is the image generated by the generative network or the original high-quality image at multiple scales.</p>
</list-item>
<list-item>
<p>An improved loss function of the generative adversarial network is also proposed to provide a more accurate measurement of the difference between the enhanced image and the high-quality image. This improvement involves incorporating the total variation loss into the traditional loss function. By considering the difference between adjacent image pixels, the total variation loss promotes image smoothness and enhances the overall quality of the generated image.</p>
</list-item>
</list>
</sec>
<sec id="s2">
<label>2</label>
<title>Related works</title>
<p>In recent years, a number of underwater image enhancement methods have been proposed. These methods can be broadly classified into three categories: model-free methods, model-based methods, and deep learning-based methods. The model-free methods do not require a degradation model for underwater images. They correct the color and improve the contrast of underwater images by directly adjusting the image pixel values (<xref ref-type="bibr" rid="B34">Zhang et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B39">Zhuang et&#xa0;al., 2021</xref>). While the model-free method can effectively correct image color, it struggles to address issues such as blurred details and noise interference. Furthermore, these methods typically involve multiple steps to process images, making practical applications challenging. In contrast, model-based methods establish a degradation model for underwater images and estimate model parameters using prior knowledge. These methods obtain enhanced images by inversion of the model (<xref ref-type="bibr" rid="B3">Ding et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B38">Zhou et&#xa0;al., 2022</xref>). These model-based methods exhibit superior performance in terms of color correction. Nevertheless, a majority of these methods rely on scene-specific depth and illumination information as <italic>a priori</italic> knowledge to estimate the model parameters. This dependence on such information is less stable and cannot be easily adapted to varying underwater scenes.</p>
<p>Recently, deep learning technology has developed rapidly. It has been widely used in image dehazing (<xref ref-type="bibr" rid="B19">Liu W. et&#xa0;al., 2019</xref>; <xref ref-type="bibr" rid="B28">Wang et&#xa0;al., 2022</xref>), super-resolution (<xref ref-type="bibr" rid="B23">Srivastava et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B24">Tian et&#xa0;al., 2022</xref>), remotely sensed image enhancement (<xref ref-type="bibr" rid="B10">Huang et&#xa0;al., 2022</xref>), and underwater image enhancement (<xref ref-type="bibr" rid="B16">Li et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B37">Zhou et&#xa0;al., 2023</xref>). It uses a large number of degraded images and high-quality images to train the network model without constructing the degradation model. Therefore, it is more suitable for different underwater environments. Compared with traditional deep learning with a single network, generative adversarial networks consist of two networks, the generative network and the adversarial network. The adversarial network can indirectly improve the performance of the generative network. Due to the advantages of a generative adversarial network, it is widely used in underwater image enhancement. Fabbri et&#xa0;al. proposed UGAN (<xref ref-type="bibr" rid="B5">Fabbri et&#xa0;al., 2018</xref>). They used CycleGAN to generate paired underwater image datasets for the following network training. Meanwhile, they added L1 loss and gradient loss to the original loss of Wasserstein GAN to better restore the degraded underwater images. This method can well correct the color of underwater images, but the model has some limitations in the types of images. Liu et&#xa0;al. proposed MLFcGAN (<xref ref-type="bibr" rid="B19">Liu X. et&#xa0;al., 2019</xref>). The network extracted multi-scale features and enhanced local features by using global features. The network was effective in restoring underwater image colors and eliminating unwanted artifacts but performed poorly in restoring image texture details. Guo et&#xa0;al. proposed a multi-scale dense generative adversarial network (<xref ref-type="bibr" rid="B7">Guo et&#xa0;al., 2019</xref>). This network improved its performance through the design of a multi-scale dense module, alongside the incorporation of L1 loss and gradient loss. These additions enabled the network to generate images of superior quality. While this method demonstrated strong results with both synthetic and real underwater images, it falls short in producing aesthetically pleasing underwater images.</p>
<p>Yang et&#xa0;al. proposed an underwater image enhancement method based on conditional generative adversarial networks (<xref ref-type="bibr" rid="B32">Yang et&#xa0;al., 2020</xref>). The network employed a dual discriminator that guided the generator to generate higher-quality images in terms of both global semantics and local features. Islam et&#xa0;al. proposed a fast underwater enhancement method (<xref ref-type="bibr" rid="B13">Islam et&#xa0;al., 2020</xref>). The method used a CGAN-based network model with L1 loss and Perceptual loss as loss functions. It showed good enhancement on the EUVP dataset but was less effective for enhancing images with severe degradation. Wu et&#xa0;al. proposed a multi-scale fusion generative adversarial network (<xref ref-type="bibr" rid="B29">Wu et&#xa0;al., 2022</xref>). To help the model achieve better performance, the network used three prior images as input to refine the prior features and then these features are fused into the encoding and decoding process. Jiang et&#xa0;al. proposed a target-oriented perceptual fusion generative adversarial network (<xref ref-type="bibr" rid="B14">Jiang et&#xa0;al., 2022</xref>). The network used a Multi-scale Dense Boosted module and Deep Aesthetic Render module for contrast enhancement and color correction. A dual discriminator for global-local discrimination was used, too. Liu R. et&#xa0;al. proposed an unsupervised model to enhance underwater images (<xref ref-type="bibr" rid="B18">Liu et&#xa0;al., 2022</xref>). They constructed a twin adversarial constrained enhancement module to eliminate the reliance on paired images. It showed good performance in improving image quality.</p>
<p>Although underwater image enhancement based on generative adversarial networks attempts to improve the quality of underwater images, the enhanced underwater images still contain much color distortion and detail loss, which affect the performance of high-level computer vision for analysis of underwater images.</p>
</sec>
<sec id="s3">
<label>3</label>
<title>Proposed method</title>
<p>To improve the quality of the enhanced underwater images, a generative adversarial network for enhancing underwater images is proposed. A generative adversarial network consists of a generative network and an adversarial network. The generative network is responsible for enhancing degraded underwater images, aiming to produce visually improved outputs. It takes degraded underwater images as input and generates enhanced versions of those images. The adversarial network plays a crucial role in evaluating the performance of the generative network. It serves as a discriminator and is responsible for determining whether an input image belongs to the set of generated images produced by the generative network or the original high-quality images. The adversarial component guides and offers feedback to the generative network, promoting its improvement by differentiating between real and generated images. Through the interaction of the generative and adversarial networks, the proposed GAN framework strives to augment the quality of underwater images. This is achieved by training the generative network to generate visually appealing and realistic outputs, with the adversarial network providing feedback to refine its performance.</p>
<sec id="s3_1">
<label>3.1</label>
<title>Generative network</title>
<p>The proposed generative network consists of three primary modules: a residual module, a multi-scale dilated convolution module, and an attention module. The structure of the generative network is illustrated in <xref ref-type="fig" rid="f1">
<bold>Figure&#xa0;1</bold>
</xref>. Firstly, a convolutional layer coupled with the LeakyReLU activation function is employed to extract local features. The number of channels also increases from 3 to 8. Secondly, two designed residual modules are used to reduce the size of feature maps and extract feature maps with different scales. The residual module reduces the output feature map size to one-half of the input feature map size. The number of channels of the output feature maps for the two residual modules are 32 and 128, respectively. Thirdly, two designed multi-scale dilated convolution modules are used to expand the receptive field and extract multi-scale features without changing the number of channels and the size of the feature map. Fourthly, we use deconvolution to increase the size of the feature map. In contrast to the conventional upsampling operation, deconvolution allows for the learning of parameters, which aids in recovering feature information. Besides, a new attention module is proposed and used to extract important features that are beneficial for enhancing underwater images. In the end, the extracted feature maps are restored to an RGB image using a convolution layer and a Tanh activation function. This restored underwater image is the enhanced underwater image.</p>
<fig id="f1" position="float">
<label>Figure&#xa0;1</label>
<caption>
<p>The proposed generative network.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1226024-g001.tif"/>
</fig>
<p>In conventional generative networks, multiple downsampling is employed to broaden the receptive field and extract feature information on different scales. The downsampling will lead to the loss of information, which reduces the quality of the enhanced image. To reduce the loss of information, we design a residual module and use the designed residual module to realize the downsampling operation. In the designed generative network, two designed residual modules are used to expand the receptive field and extract multi-scale feature information. The structure of the proposed designed residual module is illustrated in <xref ref-type="fig" rid="f2">
<bold>Figure&#xa0;2</bold>
</xref>. It consists of two branches. The upper branch consists of a 4&#xd7;4 convolution layer with stride 1, an instance normalization layer, a LeakyReLU activation function, a 4&#xd7;4 convolution layer with stride 2, and an instance normalization layer. The first 4&#xd7;4 convolution layer is used to increase the number of channels without changing the size of the feature map. The instance normalization layer is used to improve network stability and speed up network convergence. The second 4&#xd7;4 convolution layer is used to decrease the size of feature maps, instead of pooling operation for downsampling. In the lower branch, a 1&#xd7;1 convolution layer with stride 2 is used to directly decrease the size of feature maps. The output feature maps of two branches are fused by the element addition operation.</p>
<fig id="f2" position="float">
<label>Figure&#xa0;2</label>
<caption>
<p>The proposed residual module.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1226024-g002.tif"/>
</fig>
<p>A larger receptive field proves advantageous for extracting global features, whereas a smaller receptive field is well-suited for extracting local texture features. To extract more comprehensive information, we have designed a multi-scale dilated convolution module. This module integrates five distinct receptive fields, allowing it to extract features across various scales simultaneously. The architecture of the proposed multi-scale dilated convolution module is illustrated in <xref ref-type="fig" rid="f3">
<bold>Figure&#xa0;3</bold>
</xref>. It consists of five branches. The first branch only contains a 1&#xd7;1 convolution with a LeakyReLU activation function. The second branch contains a 5&#xd7;5 convolution with a LeakyReLU activation function, a 3&#xd7;3 dilated convolution with dilated rate 5, an instance normalization, and a LeakyReLU activation function. The third branch contains a 3&#xd7;3 convolution with a LeakyReLU activation function, a 3&#xd7;3dilated convolution with dilated rate 3, an instance normalization, and a LeakyReLU activation function. The fourth branch contains a 5&#xd7;5 convolution with a LeakyReLU activation function. The fifth branch contains a 3&#xd7;3 convolution with a LeakyReLU activation function. The receptive fields for the five branches are 1&#xd7;1, 15&#xd7;15, 9&#xd7;9, 5&#xd7;5 and 3&#xd7;3, respectively. The output feature maps of the second branch to the fifth branch are fused by the concatenation operation. The last 1&#xd7;1 convolution layer is used to adjust the number of channels of the fused feature map to be equal to the number of channels in the first branch. In the end, the output feature maps of the last 1&#xd7;1 convolution and the first branch are fused by an element-wise addition operation.</p>
<fig id="f3" position="float">
<label>Figure&#xa0;3</label>
<caption>
<p>The proposed multi-scale dilated convolution module.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1226024-g003.tif"/>
</fig>
<p>For the extraction of crucial features that contribute to the enhancement of underwater images, an attention module has been introduced, as depicted in <xref ref-type="fig" rid="f4">
<bold>Figure&#xa0;4</bold>
</xref>. This module comprises three key components: a texture encoding module, a feature extraction module, and an attention generation module. The texture encoding module consists of three branches. The first branch only contains a 1&#xd7;1 convolution layer that is used to encode features in channel dimension. The second branch contains a 1&#xd7;1 convolution layer, an average pooling in the horizontal direction, and a permute operation. The convolution layer is used to adjust the number of channels. The average pooling is used to encode the features along the horizontal direction. The permute operation is used to rearrange the dimensions of the feature maps. The third branch contains a 1&#xd7;1 convolution layer, an average pooling in the vertical direction, and a permute operation. The average pooling is used to encode the features along the vertical direction. In the end, the output feature maps of three branches are concatenated by the concatenate operation. The size of the feature map of the texture encoding module is 3&#xd7;H&#xd7;W. The feature extraction module contains a 1&#xd7;1 convolution with a LeakyReLU activation function to extract features. The attention generation module contains three branches that contain a permute operation, a 1&#xd7;1convolution, and a sigmoid function. The permute operation is to rearrange the dimensions of the feature maps. The 1&#xd7;1 convolution is used to adjust the number of channels. The sigmoid function is used to generate weight. Utilizing the attention generation module, three weights are derived for the channel dimension, vertical dimension, and horizontal dimension. Eventually, these three weights are applied as multipliers to the input feature map, resulting in the production of the output feature map.</p>
<fig id="f4" position="float">
<label>Figure&#xa0;4</label>
<caption>
<p>The proposed attention module.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1226024-g004.tif"/>
</fig>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Discriminative network</title>
<p>A multi-scale adversarial network based on the Markovian adversarial network is proposed and shown in <xref ref-type="fig" rid="f5">
<bold>Figure&#xa0;5</bold>
</xref>. It consists of 5 layers of downsampling. The downsampling operation is implemented by the residual module to reduce the loss of feature information. To improve the multi-scale feature extraction capability of the adversarial network, the concatenation operation is employed to fuse the features obtained from three residual modules at different scales. Furthermore, we use the convolution operation to adjust the number of channels in the output feature maps of the 4th and 5th residual modules to 1, respectively. In the end, we get the two judgment scores from two adjusted output feature maps. The weights of the two scores are 0.6 and 0.4, respectively.</p>
<fig id="f5" position="float">
<label>Figure&#xa0;5</label>
<caption>
<p>The proposed adversarial network.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1226024-g005.tif"/>
</fig>
</sec>
<sec id="s3_3">
<label>3.3</label>
<title>Loss function</title>
<p>An improved loss function is proposed by introducing the total variation loss into the conventional loss function. The improved loss function is expressed as follows.</p>
<disp-formula>
<label>(1)</label>
<mml:math display="block" id="M1">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mn>0.6</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>+</mml:mo>
<mml:mn>0.4</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im1">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula>
<mml:math display="inline" id="im2">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula>
<mml:math display="inline" id="im3">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula>
<mml:math display="inline" id="im4">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are scaling coefficients to adjust the importance of each loss function. We initially set the coefficient initial values based on the importance of the function, where the higher importance of the function corresponds to a larger coefficient value. We randomly set the coefficient initial values to <inline-formula>
<mml:math display="inline" id="im5">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mn>0.2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>; <inline-formula>
<mml:math display="inline" id="im56">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mn>0.4</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, 0.42, 0.44, 0.46, 0.48, or 0.5; and <inline-formula>
<mml:math display="inline" id="im7">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.2, 0.19, 0.18, 0.17, 0.16, or 0.15; and <inline-formula>
<mml:math display="inline" id="im6">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mn>0.2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, 0.19, 0.18, 0.17, 0.16, or 0.15. In our experiments, when <inline-formula>
<mml:math display="inline" id="im8">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mn>0.2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula>
<mml:math display="inline" id="im9">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mn>0.48</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula>
<mml:math display="inline" id="im10">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mn>0.16</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula>
<mml:math display="inline" id="im11">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mn>0.16</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, our proposed method has better performance in enhancing underwater images. Therefore, we set <inline-formula>
<mml:math display="inline" id="im12">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mn>0.2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula>
<mml:math display="inline" id="im13">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mn>0.48</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula>
<mml:math display="inline" id="im14">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mn>0.16</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula>
<mml:math display="inline" id="im15">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mn>0.16</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>. <inline-formula>
<mml:math display="inline" id="im16">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mo>&#xb7;</mml:mo>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> is the adversarial loss function, which is calculated as follows.</p>
<disp-formula>
<label>(2)</label>
<mml:math display="block" id="M2">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>Y</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">[</mml:mo>
<mml:mi>log</mml:mi>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>X</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo stretchy="false">]</mml:mo>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>Y</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">[</mml:mo>
<mml:mi>log</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>X</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>,</mml:mo>
<mml:mi>X</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula>
<label>(3)</label>
<mml:math display="block" id="M3">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>Y</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">[</mml:mo>
<mml:mi>log</mml:mi>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>X</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo stretchy="false">]</mml:mo>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>Y</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">[</mml:mo>
<mml:mi>log</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>X</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>,</mml:mo>
<mml:mi>X</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im17">
<mml:mi>X</mml:mi>
</mml:math>
</inline-formula> is the low-quality underwater image, <inline-formula>
<mml:math display="inline" id="im18">
<mml:mi>Y</mml:mi>
</mml:math>
</inline-formula> is the high-quality underwater image, <inline-formula>
<mml:math display="inline" id="im19">
<mml:mi>G</mml:mi>
</mml:math>
</inline-formula> is the generator, <inline-formula>
<mml:math display="inline" id="im20">
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>X</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> is the output of the generator, <inline-formula>
<mml:math display="inline" id="im21">
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mo>&#xb7;</mml:mo>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> is the first output score of the discriminator, and <inline-formula>
<mml:math display="inline" id="im22">
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mo>&#xb7;</mml:mo>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> is the second output score of the discriminator. <inline-formula>
<mml:math display="inline" id="im23">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> is the L1 loss function, which is expressed as follows.</p>
<disp-formula>
<label>(4)</label>
<mml:math display="block" id="M4">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>Y</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">[</mml:mo>
<mml:mo>|</mml:mo>
<mml:mo>|</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>X</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>|</mml:mo>
<mml:msub>
<mml:mo>|</mml:mo>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
<p>
<inline-formula>
<mml:math display="inline" id="im24">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> is the perceptual loss function, which is expressed as follows.</p>
<disp-formula>
<label>(5)</label>
<mml:math display="block" id="M5">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>Y</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">[</mml:mo>
<mml:mo>|</mml:mo>
<mml:mo>|</mml:mo>
<mml:mi>&#x3d5;</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>&#x3d5;</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>X</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>|</mml:mo>
<mml:msub>
<mml:mo>|</mml:mo>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im25">
<mml:mrow>
<mml:mi>&#x3d5;</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mo>&#xb7;</mml:mo>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> are the high-level features extracted by a pre-trained VGG-19 network. The total variation loss is expressed as follows.</p>
<disp-formula>
<label>(6)</label>
<mml:math display="block" id="M6">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>X</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mstyle displaystyle="true">
<mml:munder>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:munder>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
<mml:mo>+</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>+</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>+</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mstyle scriptlevel="+1">
<mml:mfrac>
<mml:mi>&#x3b2;</mml:mi>
<mml:mn>2</mml:mn>
</mml:mfrac>
</mml:mstyle>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mstyle>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im26">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the pixel in the ith row and the jth column of the enhanced image that is the <inline-formula>
<mml:math display="inline" id="im27">
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>X</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Simulation and discussion</title>
<p>In this section, we use a synthetic paired underwater image dataset and a real underwater image dataset to test the effectiveness of our proposed method through qualitative and quantitative experiments. We compared our method with four underwater image enhancement methods: the FUnIEGAN (<xref ref-type="bibr" rid="B13">Islam et&#xa0;al., 2020</xref>), the FWGAN (<xref ref-type="bibr" rid="B29">Wu et&#xa0;al., 2022</xref>), the TOPAL (<xref ref-type="bibr" rid="B14">Jiang et&#xa0;al., 2022</xref>) and the TACL (<xref ref-type="bibr" rid="B18">Liu et&#xa0;al., 2022</xref>). We evaluated each method quantitatively using two full-reference evaluation metrics which were peak signal-to-noise ratio (PSNR), structural similarity (SSIM, <xref ref-type="bibr" rid="B27">Wang et&#xa0;al., 2004</xref>), and one no-reference evaluation metric which was underwater image quality measures (UIQM,<xref ref-type="bibr" rid="B22">Panetta et&#xa0;al., 2015</xref>).</p>
<sec id="s4_1">
<label>4.1</label>
<title>Datasets and metrics</title>
<p>The underwater ImageNet dataset (<xref ref-type="bibr" rid="B5">Fabbri et&#xa0;al., 2018</xref>) which contains 6,128 pairs of underwater images is used as the training set. Fabbri et&#xa0;al., first selected underwater images from the ImageNet dataset, and secondly classified the selected underwater images into degraded underwater images and high-quality underwater images. Thirdly, CycleGAN was trained on these images and used to generate 6,128 pairs of high-quality underwater images and their corresponding degraded underwater images. The EUVP dataset (<xref ref-type="bibr" rid="B13">Islam et&#xa0;al., 2020</xref>) which contains paired images, and the UIEB dataset (<xref ref-type="bibr" rid="B15">Li et&#xa0;al., 2019</xref>), which contains real-world underwater images, were used to test the performance of different methods, respectively. The PSNR, SSIM, and UIQM were evaluation metrics. The PSNR is expressed as follows.</p>
<disp-formula>
<label>(7)</label>
<mml:math display="block" id="M7">
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mi>S</mml:mi>
<mml:mi>N</mml:mi>
<mml:mi>R</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>x</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>y</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mn>10</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>log</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">[</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mn>255</mml:mn>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>S</mml:mi>
<mml:mi>E</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>x</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>y</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mfrac>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im28">
<mml:mi>x</mml:mi>
</mml:math>
</inline-formula> and <inline-formula>
<mml:math display="inline" id="im29">
<mml:mi>y</mml:mi>
</mml:math>
</inline-formula> are the enhanced image and the corresponding ground truth image. MSE is the mean square error. It is expressed as follows.</p>
<disp-formula>
<label>(8)</label>
<mml:math display="block" id="M8">
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>S</mml:mi>
<mml:mi>E</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:munderover>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:munderover>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mstyle>
</mml:mrow>
</mml:mstyle>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im30">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is a pixel of enhanced image <inline-formula>
<mml:math display="inline" id="im31">
<mml:mi>x</mml:mi>
</mml:math>
</inline-formula>, <inline-formula>
<mml:math display="inline" id="im32">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is a pixel of the ground truth image <inline-formula>
<mml:math display="inline" id="im33">
<mml:mi>y</mml:mi>
</mml:math>
</inline-formula>. The larger the value of PSNR is, the closer the enhanced image is to the ground truth image. The SSIM is expressed as follows.</p>
<disp-formula>
<label>(9)</label>
<mml:math display="block" id="M9">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>S</mml:mi>
<mml:mi>I</mml:mi>
<mml:mi>M</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>x</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>y</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>y</mml:mi>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>x</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>+</mml:mo>
<mml:msubsup>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>y</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>x</mml:mi>
<mml:mi>y</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>x</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>+</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>y</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im34">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula>
<mml:math display="inline" id="im35">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>y</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the mean of <inline-formula>
<mml:math display="inline" id="im36">
<mml:mi>x</mml:mi>
</mml:math>
</inline-formula> and <inline-formula>
<mml:math display="inline" id="im37">
<mml:mi>y</mml:mi>
</mml:math>
</inline-formula>, respectively. The <inline-formula>
<mml:math display="inline" id="im38">
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>x</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula>
<mml:math display="inline" id="im39">
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>y</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> are the variance of <inline-formula>
<mml:math display="inline" id="im40">
<mml:mi>x</mml:mi>
</mml:math>
</inline-formula> and <inline-formula>
<mml:math display="inline" id="im41">
<mml:mi>y</mml:mi>
</mml:math>
</inline-formula>, respectively. The <inline-formula>
<mml:math display="inline" id="im42">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>x</mml:mi>
<mml:mi>y</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the covariance of <inline-formula>
<mml:math display="inline" id="im43">
<mml:mi>x</mml:mi>
</mml:math>
</inline-formula> and <inline-formula>
<mml:math display="inline" id="im44">
<mml:mi>y</mml:mi>
</mml:math>
</inline-formula>. The closer the SSIM value is to 1, the closer the enhanced image is to the ground truth image.</p>
<p>The UIQM consists of three parts, which are UICM (underwater image colorfulness measure), UISM (underwater image sharpness measure), and UIConM (underwater image contrast measure). It is expressed as follows.</p>
<disp-formula>
<label>(10)</label>
<mml:math display="block" id="M10">
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>I</mml:mi>
<mml:mi>Q</mml:mi>
<mml:mi>M</mml:mi>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mi>U</mml:mi>
<mml:mi>I</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>M</mml:mi>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mi>U</mml:mi>
<mml:mi>I</mml:mi>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mi>U</mml:mi>
<mml:mi>I</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im45">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>=0.0282, <inline-formula>
<mml:math display="inline" id="im46">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>=0.2953, and <inline-formula>
<mml:math display="inline" id="im47">
<mml:mrow>
<mml:msub>
<mml:mi>c</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>=3.5753. The higher the UIQM value is, the better the color balance, sharpness, and contrast of the enhanced image are.</p>
</sec>
<sec id="s4_2">
<label>4.2</label>
<title>Underwater image enhancement on synthetic images</title>
<p>We evaluated the performance of our proposed method on the synthetic images using the test_samples subset from the EUVP dataset. This subset consisted of 515 pairs of underwater degraded images along with their corresponding high-quality images. We randomly selected three paired images that consisted of reference images (high-quality images) and corresponding degraded images that were synthesized to test the performances of FUnIEGAN, FWGAN, TOPAL, TACL, and our method. The reference underwater images (high-quality underwater images), raw images (degraded underwater images), and underwater images enhanced by different methods are shown in <xref ref-type="fig" rid="f6">
<bold>Figure&#xa0;6</bold>
</xref>. In the first row, the FUnIEGAN method introduces noise interference in the enhanced images, which negatively affects their quality. The FWGAN cannot effectively enhance the contrast. The TOPAL method fails to adequately restore the details in the enhanced images, leading to a loss of important visual information. The TACL method produces reddish color biases in the enhanced images, which deviates from the desired color accuracy and may impact the overall visual quality. The image enhanced by our method stands out due to its exceptional color correction and contrast enhancement. In the second row, the FUnIEGAN method introduces artifacts in the enhanced image, negatively impacting its visual quality. The FWGAN method, although improving the image, still leaves a residual haze effect. However, the TACL, TOPAL, and our proposed method effectively enhance the image details, resulting in sharper visual features. Nonetheless, our approach excels in terms of color fidelity, yielding a more authentic and natural color rendition in the enhanced image. In the third row, the FUnIEGAN method introduces reddish color biases to the enhanced image, which diverges from the original color representation. The FWGAN method fails to provide clear details in the enhanced image, resulting in reduced clarity. Both the TOPAL and TACL methods leave a residual haze effect on the enhanced images, diminishing their overall quality. Conversely, our proposed method produces enhanced images that closely resemble the reference image, demonstrating better color accuracy and preserving finer details.</p>
<fig id="f6" position="float">
<label>Figure&#xa0;6</label>
<caption>
<p>The images enhanced by different methods from the EUVP dataset.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1226024-g006.tif"/>
</fig>
<p>In summary, the FUnIEGAN method falls short in effectively enhancing degraded underwater images and addressing issues related to color bias and image details. The FWGAN, TOPAL, and TACL methods struggle to adequately sharpen image details. In contrast, our proposed method successfully generates enhanced images that demonstrate satisfactory color correction, contrast enhancement, and detail sharpening. Furthermore, the images enhanced by our method closely resemble the corresponding reference images, indicating its superior performance.</p>
<p>To quantitatively analyze the performance of different methods, we used all paired images in the EUVP test set as test images and computed the PSNR, SSIM, and UIQM of the images enhanced by different methods. The average results are shown in <xref ref-type="table" rid="T1">
<bold>Table&#xa0;1</bold>
</xref> The PSNR values for the FUnIEGAN method, FWGAN method, TOPAL method, TACL method, and our proposed method were 23.23, 26.87, 25.41, 26.65, and 27.28, respectively. Our proposed method had the highest PSNR, followed by the FWGAN method and TACL method. The SSIM values for the FUnIEGAN method, FWGAN method, TOPAL method, TACL method, and our proposed method were 0.70, 0.80, 0.76, 0.79 and 0.81, respectively. Our proposed method had the highest SSIM, followed by the FWGAN method and TACL method. The UIQM values for the FUnIEGAN method, FWGAN method, TOPAL method, TACL method, and our proposed method were 3.04, 2.97, 3.06, 2.95, and 3.14, respectively. Our proposed method had the highest UIQM, followed by the FUnIEGAN method and TOPAL method. As shown in <xref ref-type="table" rid="T1">
<bold>Table&#xa0;1</bold>
</xref>, our proposed method had the highest PSNR, SSIM, and UIQM, which shows that our proposed method had the best performance in enhancing underwater images on the EUVP dataset.</p>
<table-wrap id="T1" position="float">
<label>Table&#xa0;1</label>
<caption>
<p>Performances of underwater image enhancement for different methods on the EUVP dataset.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center"/>
<th valign="middle" align="center">FUnIEGAN</th>
<th valign="middle" align="center">FWGAN</th>
<th valign="middle" align="center">TOPAL</th>
<th valign="middle" align="center">TACL</th>
<th valign="middle" align="center">Ours</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" align="center">PSNR</td>
<td valign="middle" align="center">23.23</td>
<td valign="middle" align="center">26.87</td>
<td valign="middle" align="center">25.41</td>
<td valign="middle" align="center">26.65</td>
<td valign="middle" align="center">28.28</td>
</tr>
<tr>
<td valign="middle" align="center">SSIM</td>
<td valign="middle" align="center">0.70</td>
<td valign="middle" align="center">0.80</td>
<td valign="middle" align="center">0.76</td>
<td valign="middle" align="center">0.79</td>
<td valign="middle" align="center">0.85</td>
</tr>
<tr>
<td valign="middle" align="center">UIQM</td>
<td valign="middle" align="center">3.04</td>
<td valign="middle" align="center">2.97</td>
<td valign="middle" align="center">3.06</td>
<td valign="middle" align="center">2.95</td>
<td valign="middle" align="center">3.25</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s4_3">
<label>4.3</label>
<title>Underwater image enhancement on real-world images</title>
<p>We also assessed the effectiveness of our proposed method using 950 real-world images sourced from the UIEB dataset. This dataset encompasses a total of 950 underwater images in degraded conditions, consisting of 890 images from the raw-890 subset and an additional 60 images from the challenging-60 subset. We randomly selected three real-world degraded underwater images from the raw-890 subset to evaluate the performances of FUnIEGAN, FWGAN, TOPAL, TACL, and our proposed method. The images included both the original degraded underwater images and the corresponding enhanced underwater images generated by each method. The results are visualized in <xref ref-type="fig" rid="f7">
<bold>Figure&#xa0;7</bold>
</xref>. In the first row, the images enhanced by FUnIEGAN, FWGAN, and TACL exhibit reddish color biases, while the image enhanced by TOPAL shows greenish color biases. In contrast, the image enhanced by our proposed method achieves satisfactory contrast and saturation. In the second row, the image enhanced by FUnIEGAN exhibits checkerboard artifacts. The image enhanced by the FWGAN suffers from bluish color bias. The image enhanced by the TOPAL suffers from greenish color bias. TACL generates a darkish image. In contrast, our proposed method effectively removes the bluish hue, resulting in a more accurate and visually pleasing enhanced image. In the third row, the image enhanced by FUnIEGAN exhibits artifacts. The images enhanced by FWGAN and TACL suffer from reddish color bias. TOPAL fails to effectively sharpen details in the enhanced image. In contrast, our proposed method successfully enhances the images in terms of color correction and detail sharpening.</p>
<fig id="f7" position="float">
<label>Figure&#xa0;7</label>
<caption>
<p>The images enhanced by different methods from the UIEB dataset.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1226024-g007.tif"/>
</fig>
<p>In summary, the FUnIEGAN usually introduces color bias and artifacts in the enhanced image. The FWGAN, TOPAL, and TACL cannot effectively correct color and sharpen details. The results show that our method has the best generalization capability for real-world underwater image enhancement.</p>
<p>To quantitatively analyze the performance of different methods, we used all real-world degraded underwater images on the UIEB dataset as test images and computed the UICM, UISM, UIConM, and UIQM. The UICM, UISM, and UIConM are used to measure the colorfulness, sharpness, and contrast of enhanced underwater images, respectively. The UIQM which consists of UICM, UISM, and UIConM is used to measure the complete visual effect of enhanced underwater images. The average results are shown in <xref ref-type="table" rid="T2">
<bold>Table&#xa0;2</bold>
</xref>. The UICM values for the FUnIEGAN method, FWGAN method, TOPAL method, TACL method, and our proposed method were 4.41, 4.43, 4.93, 4.68, and 5.02, respectively. Our proposed method had the highest UICM, followed by the TOPAL method and TACL method, which shows that our method had the best performance in restoring colorfulness. The UISM values for the FUnIEGAN method, FWGAN method, TOPAL method, TACL method, and our proposed method were 5.82, 5.99, 6.29, 6.16, and 6.68, respectively. Our proposed method had the highest UISM, followed by the TOPAL method and TACL method, which shows that our method had the best performance in restoring sharpness. The UIConM values for the FUnIEGAN method, FWGAN method, TOPAL method, TACL method, and our proposed method were 0.24, 0.24, 0.26, 0.27, and 0.28, respectively. Our proposed method had the largest UIConM, followed by the TOPAL method and TACL method, which shows that our method had the best performance in restoring contrast. The UIQM values for the FUnIEGAN method, FWGAN method, TOPAL method, TACL method, and our proposed method were 2.70, 2.78, 2.93, 2.91, and 3.12, respectively.</p>
<table-wrap id="T2" position="float">
<label>Table&#xa0;2</label>
<caption>
<p>Performances of underwater image enhancement for different methods on the UIEB dataset.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" align="center"/>
<th valign="middle" align="center">FUnIEGAN</th>
<th valign="middle" align="center">FWGAN</th>
<th valign="middle" align="center">TOPAL</th>
<th valign="middle" align="center">TACL</th>
<th valign="middle" align="center">Ours</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="center">UICM</td>
<td valign="top" align="center">4.41</td>
<td valign="top" align="center">4.43</td>
<td valign="top" align="center">4.93</td>
<td valign="top" align="center">4.68</td>
<td valign="top" align="center">5.52</td>
</tr>
<tr>
<td valign="top" align="center">UISM</td>
<td valign="top" align="center">5.82</td>
<td valign="top" align="center">5.99</td>
<td valign="top" align="center">6.29</td>
<td valign="top" align="center">6.16</td>
<td valign="top" align="center">6.68</td>
</tr>
<tr>
<td valign="top" align="center">UIConM</td>
<td valign="top" align="center">0.24</td>
<td valign="top" align="center">0.24</td>
<td valign="top" align="center">0.26</td>
<td valign="top" align="center">0.27</td>
<td valign="top" align="center">0.31</td>
</tr>
<tr>
<td valign="top" align="center">UIQM</td>
<td valign="top" align="center">2.70</td>
<td valign="top" align="center">2.78</td>
<td valign="top" align="center">2.93</td>
<td valign="top" align="center">2.91</td>
<td valign="top" align="center">3.24</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>As shown in <xref ref-type="table" rid="T3">
<bold>Table&#xa0;3</bold>
</xref>, our proposed method had the best performance in restoring colorfulness, sharpness, and contrast. Furthermore, our proposed method also had the largest UIQM, which shows that our method had the best performance in improving the visual effect of underwater images.</p>
<table-wrap id="T3" position="float">
<label>Table&#xa0;3</label>
<caption>
<p>Experimental results of the ablation study.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center"/>
<th valign="top" align="center">w/o MAN</th>
<th valign="middle" align="center">w/o MDCM</th>
<th valign="middle" align="center">w/o AM</th>
<th valign="middle" align="center">w/o TV loss</th>
<th valign="middle" align="center">Ours</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" align="center">PSNR</td>
<td valign="middle" align="center">26.97</td>
<td valign="middle" align="center">25.54</td>
<td valign="middle" align="center">27.28</td>
<td valign="middle" align="center">27.61</td>
<td valign="middle" align="center">28.28</td>
</tr>
<tr>
<td valign="middle" align="center">SSIM</td>
<td valign="middle" align="center">0.79</td>
<td valign="middle" align="center">0.77</td>
<td valign="middle" align="center">0.81</td>
<td valign="middle" align="center">0.82</td>
<td valign="middle" align="center">0.85</td>
</tr>
<tr>
<td valign="middle" align="center">UIQM</td>
<td valign="top" align="center">2.95</td>
<td valign="middle" align="center">2.97</td>
<td valign="middle" align="center">3.12</td>
<td valign="middle" align="center">3.01</td>
<td valign="middle" align="center">3.25</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s4_4">
<label>4.4</label>
<title>Ablation study</title>
<p>To analyze the contributions of the multi-scale adversarial network, the multi-scale dilated convolution module, the attention module, and the TV loss, we conducted the following ablation studies:</p>
<list list-type="bullet">
<list-item>
<p>w/o MAN: without multi-scale adversarial network</p>
</list-item>
<list-item>
<p>w/o MDCM: without multi-scale dilated convolution module;</p>
</list-item>
<list-item>
<p>w/o AM: without attention module;</p>
</list-item>
<list-item>
<p>w/o TV loss: without TV loss;</p>
</list-item>
</list>
<p>The PSNR, SSIM, and UIQM scores on the test_samples subset from the EUVP dataset are shown in <xref ref-type="table" rid="T3">
<bold>Table&#xa0;3</bold>
</xref>. As is shown in the table, our complete model achieved the best performance compared to all the ablated models, which proves the effectiveness of the multi-scale adversarial network, the multi-scale dilated convolution module, the attention module, and the TV loss.</p>
<sec id="s4_4_1">
<label>4.4.1</label>
<title>Ablation study on MAN</title>
<p>The multi-scale adversarial network is designed to improve the discriminative power, which is helpful in improving the quality of images generated by the generative network. From <xref ref-type="table" rid="T3">
<bold>Table&#xa0;3</bold>
</xref>, compared with our method without a multi-scale adversarial network, our complete method improved the PSNR, SSIM, and UIQM scores by nearly 5%, 7%, and 9%, respectively. It is shown that the multi-scale adversarial network is effective in improving the performance of the network model.</p>
</sec>
<sec id="s4_4_2">
<label>4.4.2</label>
<title>Ablation study on MDCM</title>
<p>The multi-scale dilated convolution module in the generative network is designed to increase the receptive field and extract more feature information. From <xref ref-type="table" rid="T3">
<bold>Table&#xa0;3</bold>
</xref>, compared with our method without multi-scale dilated convolution modules, our complete method improved the PSNR, SSIM, and UIQM scores by nearly 10%, 9%, and 9%, respectively. The result demonstrates the important role of the multi-scale dilated convolution module in recovering Image color and enhancing detailed information.</p>
</sec>
<sec id="s4_4_3">
<label>4.4.3</label>
<title>Ablation study on AM</title>
<p>The attention module is designed to extract important features and reduce the influence of unimportant features. From <xref ref-type="table" rid="T3">
<bold>Table&#xa0;3</bold>
</xref>, compared with our method without the attention module, our complete method improved the PSNR, SSIM, and UIQM scores by nearly 4%, 5%, and 4%, respectively. It is shown that the attention module is effective in improving the quality of images generated by our method.</p>
</sec>
<sec id="s4_4_4">
<label>4.4.4</label>
<title>Ablation study on TV loss</title>
<p>The TV loss is added to the traditional loss function to improve the visual effect of the generated images. From <xref ref-type="table" rid="T3">
<bold>Table&#xa0;3</bold>
</xref>, compared with our method without TV loss, our complete method improved the PSNR, SSIM, and UIQM scores by nearly 2%, 4%, and 7%, respectively. The TV loss improved the image visual effect by smoothing image details, so the PSNR and SSIM scores were less increased, and the UIQM score, which is more suitable for the quality of human eye vision, was increased.</p>
</sec>
</sec>
<sec id="s4_5">
<label>4.5</label>
<title>Performance of saliency detection based on enhanced underwater images</title>
<p>We also randomly selected an image from the UIEB dataset to test the performance of saliency detection (<xref ref-type="bibr" rid="B18">Liu and Yu, 2022</xref>) based on the enhanced underwater image. In <xref ref-type="fig" rid="f8">
<bold>Figure&#xa0;8</bold>
</xref>, the images in the first row are the real-world degraded underwater image (raw image) and enhanced images by FUnIEGAN, FWGAN, TOPAL, TACL, and our method. The images in the second row are the saliency probability maps by saliency detection from the images in the first row in <xref ref-type="fig" rid="f8">
<bold>Figure&#xa0;8</bold>
</xref>. All shark boundaries are not clear for the first image in the second row. The saliency detection method only detected one shark boundary from the enhanced images by TOPAL and TACL methods, respectively. While saliency detection effectively detects more shark boundaries in the enhanced images generated by FUnIEGAN, FWGAN, and our method, it is worth noting that the boundary of the shark in the upper right part of the detected image appears less distinct in the enhanced images created by the FUnIEGAN and FWGAN methods. Compared with other methods, saliency detection detected more shark boundaries and the boundaries are clearer in the enhanced image from our method. It shows that our underwater image enhancement method is more useful in improving the performance of saliency detection.</p>
<fig id="f8" position="float">
<label>Figure&#xa0;8</label>
<caption>
<p>Saliency detection based on enhanced underwater images.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1226024-g008.tif"/>
</fig>
</sec>
<sec id="s4_6">
<label>4.6</label>
<title>Model complexity analysis</title>
<p>To further prove the performance of our model, we measured its complexity using two metrics: floating point operations (FLOPs) and parameters. FLOPs quantify the amount of computation required by the model and can be used to gauge its complexity. In our analysis, we focused on the convolution layer as it contributes significantly to the computational load. The FLOPs of the convolution layer can be calculated as follows.</p>
<disp-formula>
<label>(11)</label>
<mml:math display="block" id="M11">
<mml:mrow>
<mml:mi>F</mml:mi>
<mml:mi>L</mml:mi>
<mml:mi>O</mml:mi>
<mml:mi>P</mml:mi>
<mml:mi>s</mml:mi>
<mml:mo>=</mml:mo>
<mml:mo stretchy="false">(</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mi>K</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>H</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>W</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>o</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im48">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the number of input feature map channels, <inline-formula>
<mml:math display="inline" id="im49">
<mml:mi>K</mml:mi>
</mml:math>
</inline-formula> is the size of the convolution kernel, <inline-formula>
<mml:math display="inline" id="im50">
<mml:mi>H</mml:mi>
</mml:math>
</inline-formula>, <inline-formula>
<mml:math display="inline" id="im51">
<mml:mi>W</mml:mi>
</mml:math>
</inline-formula>, <inline-formula>
<mml:math display="inline" id="im52">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>o</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the height, width, and channels of the output feature map. The parameters of the convolution layer can be calculated as follows.</p>
<disp-formula>
<label>(12)</label>
<mml:math display="block" id="M12">
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>o</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mi>K</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im53">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula>
<mml:math display="inline" id="im54">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>o</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the number of input and output channels, <inline-formula>
<mml:math display="inline" id="im55">
<mml:mi>K</mml:mi>
</mml:math>
</inline-formula> is the size of the convolution kernel. Among them, the smaller the FLOPs, the smaller the computational complexity of the model. The fewer the parameters, the less memory the model occupies.</p>
<p>We compared the model complexity of FUnIEGAN, FWGAN, TOPAL, and TACL and our method. The measurement results are shown in <xref ref-type="table" rid="T4">
<bold>Table&#xa0;4</bold>
</xref>. While our method had a larger number of FLOPs compared to FUnIEGAN and FWGAN, it was still smaller than TOPAL and TACL. Additionally, although our method had a larger number of parameters compared to FUnIEGAN, it was smaller than FWGAN, TOPAL, and TACL. When compared to TACL and TOPAL, which have demonstrated better performance in enhancing underwater images, our proposed method stands out with smaller values for FLOPs and parameters.</p>
<table-wrap id="T4" position="float">
<label>Table&#xa0;4</label>
<caption>
<p>Measurement of model complexity.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" align="center"/>
<th valign="middle" align="center">FUnIEGAN</th>
<th valign="middle" align="center">FWGAN</th>
<th valign="middle" align="center">TOPAL</th>
<th valign="middle" align="center">TACL</th>
<th valign="middle" align="center">Ours</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="center">FLOPs(G)</td>
<td valign="top" align="center">10.75</td>
<td valign="top" align="center">19.44</td>
<td valign="top" align="center">85.50</td>
<td valign="top" align="center">97.03</td>
<td valign="top" align="center">21.18</td>
</tr>
<tr>
<td valign="top" align="center">parameters(M)</td>
<td valign="top" align="center">7.72</td>
<td valign="top" align="center">10.51</td>
<td valign="top" align="center">30.04</td>
<td valign="top" align="center">21.29</td>
<td valign="top" align="center">7.81</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s5" sec-type="conclusions">
<label>5</label>
<title>Conclusion</title>
<p>In this article, a new generative adversarial network is proposed for enhancing underwater images. First, we designed a multi-scale dilated convolution module, attention module, and residual module, and employed these modules to construct a generative network with a U-shaped network structure. The designed generative network was utilized to enhance the underwater images. Second, we designed a multi-scale adversarial network to indirectly improve the performance of the generative network. Finally, we proposed an improved loss function for the designed generative adversarial networks by incorporating the total variation loss into the traditional loss function. We used the paired underwater images consisting of high-quality images, degraded images, and real-world underwater images to test the performance of our proposed method. Compared with the other methods, the images enhanced by our proposed method from the synthesized degraded underwater images had the highest PSNR, SSIM, and UIQM. The images enhanced by our proposed method from the real-world degraded underwater images also had the highest UICM, UISM, UIConM, and UIQM. These show that the quality and visualization of enhanced underwater images from our method are better than other methods. Furthermore, ablation studies on the network structure and loss function demonstrated the effectiveness of our method. Moreover, we also used the underwater image enhancement method as a pre-processing method for saliency detection. The saliency detection results indicated that our proposed method outperforms other methods in terms of saliency detection performance. Our proposed method can improve the performance of high-level image processing. In the final analysis, we performed a thorough complexity assessment of the proposed network model. The results conclusively show that our method demonstrated lower complexity and required less memory compared to alternative approaches.</p>
</sec>
<sec id="s6" sec-type="data-availability">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s7" sec-type="author-contributions">
<title>Author contributions</title>
<p>ZW performed the experiments and wrote the manuscript. LZ and TZ revised the manuscript. YJ and YC provided the ideas and revised the article. LZ provided advice and GPU devices for parallel computing. All authors contributed to the article and approved the submitted version.</p>
</sec>
</body>
<back>
<sec id="s8" sec-type="funding-information">
<title>Funding</title>
<p>This work was supported by the Foundation for Natural Science Foundation of Jilin Province under Grants (No. 20220101190JC), Jilin Provincial Department of Education Science and Technology Research Project (No. JJKH20230125KJ).</p>
</sec>
<sec id="s9" sec-type="COI-statement">
<title>Conflict of interest</title>
<p>Author YC was employed by the company Guangdong Power Grid Co., Ltd.</p>
<p>The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec id="s10" sec-type="disclaimer">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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