Continuous wavelet transform (CWT) is an effective signal processing tool to decompose an original signal into multidimensional signals, mainly including discrete wavelet transform and continuous wavelet transform (Liu et al., 2020b). In the CWT, the algorithm uses the selected mother wavelet to decompose the hyperspectral data into a series of wavelet coefficients of different scales, which is a linear transformation. Its transformation formula is as follows:

where f (λ) is the leaf hyperspectral reflectance, λ is the wavelength within 400–950 nm, ψ_a,b is the wavelet basis function, a is the scale factor, b is the translocation factor, and W_f(a, b) is a two-dimensional matrix, including i and j, where i represents the decomposition scale (i = 1, 2, 3, …, m) and j represents the band range of the spectrum (j = 1, 2, 3, …, n), forming an m by n matrix. In this study, the spectral data of cotton leaves at three growth stages were obtained, and each leaf sample included 106 bands. As the setting of the decomposition scale has a certain influence on spectral feature recognition (Liu et al., 2020; Lin et al., 2021), the decomposition scale in this study was set as 2¹, 2², 2³, …, 2¹⁰, scales 1–10. Among them, the decomposition scales 1–3 and 4–7 belong to low frequency and middle frequency, respectively, and the rest belong to high frequency. Sym2 was selected as the wavelet basis function, and then, a PLSR model was used to quantitatively analyze the relationship between the wavelet coefficients of each decomposition scale and the LKC so as to determine the optimal decomposition scale and effective wavelength.

Different feature selection methods lead to different features being selected. To select spectral and image features sensitive and stable to the LKC in cotton, the competitive adaptive reweighted sampling (CARS), and random frog (RF) algorithms were used in this study to screen features.

Competitive adaptive reweighted sampling selects wavelength points with a large coefficient absolute value in the model through the Monte Carlo strategy and removes wavelength points with a low weight (Sun et al., 2021). The subset with the lowest root mean squared error of cross validation (RMSECV) value is retained as the feature selection result by cross-validation. In this study, the Monte Carlo strategy was set to run 50 times, using 5-fold cross-validation.

Random frog is an algorithm to measure the importance of variables (El-Hendawy et al., 2017). The main steps are as follows: (1) a subset of initial variables containing m variables is randomly initialized, (2) variables in the initial variable subset are continuously selected into the candidate subset, and the number of variables in the candidate subset increases and decreases with the number of iterations, (3) the selection probability of each variable is calculated as a measure of the importance of the variable, and (4) the characteristic wavelength is selected according to the probability of the occurrence of recorded variables in each iteration. In this study, the selection probability of each wavelength was used to screen the feature information, and the running results are presented in descending order. The number of iterations was set as 10,000, and the selection probability thresholds of the three growth periods were 0.40, 0.21, and 0.23, respectively.

The most common gray level co-occurrence matrix (GLCM) algorithm was adopted to extract texture features (Yang et al., 2021). In this study, the energy (ENE), entropy (ENT), contrast (CON), correlation (COR), and their mean (MEA) and variance (VAR) in four directions were calculated by using the gray comatrix function. The calculation equation is shown in Table 1, where the P(i, j) is the value of the GLCM in the ith row and jth column, k is the number of gray levels in the GLCM. The gray level is 256, the step size is 1, the angle is 0°, 45°, 90°, and 135°. Finally, each characteristic wavelength grayscale image will eventually produce 24 (4 × 4 + 8) texture features.

Color moments are used to represent the color distribution in the image (Ge et al., 2021). Since the color information is mainly distributed in low-order moments, first-order moments (mean, MEA), second-order moments (variance, VAR), and third-order moments (skewness, SKE) are sufficient to express the color distribution of the image. Its formula is as follows:

where Pij is the color value of the jth pixel on the ith color channel, i is the number of color channels of the image. The image in this study is grayscale image, so i = 1; MEAi is the color mean of the ith color channel of all pixels. Finally, each characteristic wavelength grayscale image will eventually produce three color features.

Notably, the named representation of combined features is as follows: (1) The characteristic wavelength-texture feature-direction, such as 400 nm-ENE-0°, which means the texture feature is ENE in the 0° direction of the 400-nm grayscale image and (2) characteristic wavelength-color feature, such as 400-nm MEA, which means the color feature is MEA of the 400-nm grayscale image.

The total LKC in three key growth stages of cotton was measured (Table 2). The concentration gradient method (Liu et al., 2015) was used to divide the total samples into 40 calibration sets and 20 validation sets in a ratio of 2:1. The range of the K content in the calibration set including the validation set was 3.56–0.51, 2.80–0.57, and 2.30–0.40% in the three growth stages, respectively, indicating that the calibration set could well represent the entire datasets. The coefficients of variation in the calibration sets and validation sets were both between 37 and 50%, show that the LKC in cotton studied had a wide range and had good representativeness and coverage.

The single-band threshold segmentation method (Figure 3) was used to extract the average spectrum of the whole cotton leaves from hyperspectral images as the original spectrum (R) and a region of interest (ROI). The threshold was set to 0.25–0.3098, and the sample area lower than 0.25 was the background plate.

The spectral curves of cotton leaves at the three growth stages were consistent with the spectral characteristics of green plants (Figure 4). There were strong absorption peaks at 450 and 680 nm and a strong reflection peak at 550 nm. Due to the many cavities in the mesophyll sponge structure, the reflectance increases sharply near the red edge region (690–760 nm), and a highly reflective platform appears in the NIR region (760–950 nm). Among them, the spectral reflectance of cotton leaves at different growth stages differed significantly in the NIR region, which showed as boll setting stage > flowering stage > budding stage. This may be because after mid-July, the redistribution and utilization of the K nutrients during fruit development and the fluidity of potassium make the K in leaves gradually transfer to cotton bolls at the flowering and boll setting stages (Singh et al., 2019), leading to the decrease in LKC, while the lack of the K in leaves increases the thickness of leaves, and the palisade tissue and parenchymal cells shrink and partially break (Zhao et al., 2001; Ramírez-Soler et al., 2021). Finally, the spectral reflectance of the boll setting stage was higher than that of the budding stage in the NIR region.

The R spectrum of cotton leaves was decomposed by the CWT at 10 scales. Correlation analysis was performed between the wavelet coefficients generated under each decomposition scale and the LKC, and the results were expressed as the absolute value of the correlation coefficient (|R|). The correlation between the wavelet coefficient and the LKC was relatively high, especially at the flowering stage of cotton growth (Figure 5). Under the calculation of different scales and movement factors, the regions with high correlation at the budding stage are mainly focused in the range of 500–550 and 640–660 nm on the mesoscales 3–5 and 7, with the highest correlation |R| = 0.74 (Figure 5A). The flowering stage showed obvious regional distribution, with a high correlation in the low dimension on scale 3, with the highest correlation |R| = 0.86 (Figure 5B). At the boll setting stage, the high-correlation area was mainly distributed in mesoscales 3–6, and the highest correlation |R| = 0.70 (Figure 5C). In addition, the wavelengths of 500–530, 640–660, and 740–760 nm showed higher correlation in the three growth stages.

To further screen out characteristic wavelengths for the rapid estimation of the LKC in cotton, reduce the analytical dimension of spectral data and highlight the timeliness and convenience of spectral monitoring, the CARS and RF algorithms were selected to screen the R spectra and the CWT spectra (scales 1–10) of the three growth periods, and the selected characteristic wavelengths did not exceed 10. In the whole spectrum, the selected characteristic wavelengths of the three growth stages were similar, but there are significant differences in the screening methods of different characteristic wavelengths. The characteristic wavelengths selected based on the CARS algorithm were evenly distributed in the range of 400–950 nm, mainly located in the visible (500 nm), red edge (700 nm), and NIR regions (900 nm) (Figures 6A–C). The characteristic wavelengths screened by the RF algorithm were mainly concentrated in the visible and NIR regions in the whole spectrum, but more characteristic wavelengths appear in the visible region (Figures 6D–F). The characteristic wavelengths located in the visible region reflect the information of leaf pigment, especially the characteristic bands distributed near the strong absorption and reflection of chlorophyll. Red edge is closely related to the physical and chemical parameters of plants, is generally used to describe the health status of plants and is affected by leaf pigment and leaf area index. The characteristic wavelengths were in the range of 800–950 nm, reflecting the structure of cotton leaves and some water absorption.

To explore the quantitative regression relationship between cotton leaf spectral data and the LKC, a quantitative estimation model was established to realize the quantification of spectral monitoring. Using the R spectrum and CWT spectra composed of characteristic wavelengths screened by CARS and RF as independent variables and the LKC as a dependent variable, PLSR estimation models of the LKC at different growth stages were established (Table 3). The calibration and validation sets perform differently in estimating the effect of the LKC model at different growth stages and decomposition scales. At the budding stage, the model R²cal and R²val both were >0.6136 (RF-CWT-7) and 0.2675 (CARS-CWT-4). At the flowering stage, the model R²cal and R²val were >0.7311 (RF-CWT-10) and 0.6158 (CARS-CWT-2). In the boll setting period, the model R²cal and R²val were both >0.5717 (RF-CWT-3) and 0.5430 (RF-CWT-6).

The all model R²val and RMSEval results are shown in Figure 7. The results showed that compared with the R spectrum, the CWT spectra could significantly improve the prediction performance of the LKC (Figures 7D–F). The optimal estimation model of the R spectrum at the budding, flowering and boll growth stages was constructed using the characteristic wavelengths selected by the CARS algorithm, indicating that CARS had a better estimation performance than the RF algorithm, this is similar to previous studies (Sun et al., 2021). The R²val values were 0.6613, 0.753, and 0.6643 and the RMSEval values were 0.5292, 0.2202, and 0.3405, respectively. Using the multi-decomposition scale CWT method, the best decomposition scales of the three growth stages were found to be CWT-1, CWT-3 and CWT-9 spectrum (Table 3). The best estimation models for the LKC were CARS-CWT-1 at the budding stage, RF-CWT-3 at the flowering stage and CARS-CWT-9 at the boll setting stage. The R²val values were 0.7918, 0.79, and 0.808 and the RMSEval values were 0.368, 0.1987 and 0.2508, respectively (Figures 7A–C). Compared with the single R spectrum model, the improved R² values at the three growth stages were 0.13, 0.04, and 0.15, respectively. Higher R²val values and lower RMSEval values indicate that these models have a good fitting degree and accuracy, and the decomposed CWT spectra can effectively extract weak information, but there are significant differences in the prediction accuracy of the CWT spectra at different decomposition scales, and the screening results of the CARS and RF algorithms also show different model effects.

To find image features that could optimize the estimation model of the LKC in cotton, gray image databases of leaves at the budding, flowering, and boll setting stages were constructed according to the selected characteristic wavelengths (Figure 8). Among them, the number of effective characteristic wavelengths in the three growth stages are 10, 10, and 9, respectively. Therefore, the total number of grayscale images in budding, flowering, and boll setting stages are 60 × 10, 60 × 10 and 60 × 9, respectively.

After the mask processing for all images, three color features and 24 texture features of each characteristic wavelength grayscale image were successively calculated. Finally, the color and texture data extracted from the three growth periods were stored in 3 × 30 and 3 × 240 matrices, and a correlation analysis was performed with the LKC, respectively. The results are shown in Figure 10, where a square represents a feature.

For color features, the correlation between MEA and VAR was higher than that with SKE at the budding, flowering, and boll setting stages. The highest correlations of color features in the three growth stages were obtained for 532 nm-VAR (R = 0.39, p < 0.01), which reached extremely significant correlation, 461 nm-MEA (R = 0.18, p < 0.05) and 522 nm-MEA (R = −0.33, p < 0.05). The results showed that the overall brightness and color distribution of images were closely related to the LKC. The texture features with a high correlation between the budding, flowering, and boll setting stage were different. The high correlation at the budding stage was mainly the CON of 471, 512, and 641 nm grayscale images in the 90° and 135° directions, and the highest correlation was 641 nm-CON-135° (R = −0.48). The results showed that the furrow depth of the cotton leaf surface at the budding stage was negatively correlated with K content. The texture features with high correlation at the flowering stage was mainly the COR of the characteristic wavelength of visible light (e.g., 476 nm) in the direction of 135°, especially 476 nm-COR-135° (R = −0.38). During the boll setting stage, highly correlated texture features were concentrated in the CON at the characteristic wavelength of NIR (e.g., 799 nm), and the highest correlation was obtained at 799 nm-VAR (CON) (R = −0.44), indicating that the uniformity of the leaf surface texture was significantly negatively correlated with the K at the flowering and boll setting stages.

As can be seen from Figure 9, the color and texture feature dimensions of each growth period have higher dimensions and contain a large amount of invalid information. Therefore, we choose the CARS algorithm with better performance and combined correlation analysis to determine the effective image features. The screening results are shown in Table 4.

Table 5 shows the results of the PLSR estimation model of the LKC in cotton at different growth stages was created based on the combined characteristics of “CWT spectra + image.” Compared with the R spectrum and CWT spectra models, the fusion of image features can improve the accuracy of the K estimation model at the three growth stages, but the performance of models constructed based on CWT spectra fusion with either “color” or “texture” or with “color + texture” features is different. Among them, the best estimation model was “CWT-1 + texture” for the budding stage, “CWT-3 + color” for the flowering stage and “CWT-9 + texture” for the boll setting stage. Based on the “spectra + image” combination, the best estimation models of the LKC in cotton at the budding, flowering, and boll setting stages had 16, 14, and 12 features, respectively. Moreover, texture features contribute more to the model performance improvement than color features do. These results provide a reference for rapid and non-destructive monitoring of the K.

Figure 10 shows the best inversion model of the LKC in cotton at three growth stages. The optimal LKC estimation model constructed based on the characteristic wavelengths of R spectra at budding, flowering, and boll setting stages had R²val s of 0.6613, 0.7530, and 0.6643; and RMSEvals of 0.5292, 0.2202, and 0.3405, respectively (Figures 10A–C). Based on the “CWT spectra + image” feature, the accuracy R²val values of the best LKC estimation model for the three growth stages had R²val s of 0.8652, 0.8261, and 0.8952 and the RMSEval of 0.3009, 0.1821, and 0.2019, respectively (Figures 10D,F). Compared with the single R spectrum, the model accuracy R² increased by 0.2, 0.08, and 0.23, respectively, indicating the feasibility of estimating the LKC in cotton based on CWT analysis and image feature fusion and achieving high-precision and rapid monitoring. The best estimation of the LKC in cotton was at the boll setting stage. Furthermore, because the fusion image features at the flowering stage contributed little to the improvement of the model accuracy, it indicated that the quantitative inversion of the K in the growth stage could be satisfied only by R spectral data, and the model had high stability.