Quality and Stability of Compressed Sensing Schemes in the Fast Spin Echo Sequence
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1
University of Antwerp, Department of Biomedical Sciences, Belgium
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2
Iminds/Image Processing and Interpretation Research Group, University of Ghent, Belgium
While Compressed Sensing [1], [2] has been proven to be stable for truly sparse data even when noise is present, Magnetic Resonanse (MR) images are often only approximately sparse, and thus break the requirements for CS. Therefore the image cannot be reconstructed exactly, and similar compressed sensing compatible sampling schemes give different reconstructions.
The purpose of this small study was to evaluate the quality and stability of CS reconstructed images for different sets of pseudo-random schemes. To simulate a CS acquisition, MRI data was retrospectively undersampled in the phase-encoding direction using a pseudo-random scheme for speed up factors of 2, 3 and 4 (resp. 50%, 34% or 25% of the total k-space). The schemes consisted of a fully sampled block in the center of k-space, the size of which was varied between 10 to 90% of the total data sampled, and a part at the edges which was undersampled according to a probability density function which was a power law [4] with power=[2,4,7,10]. These schemes were implemented for a Fast Spin Echo (FSE) sequence, using five different strategies for dividing the phase encoding lines of the CS-scheme over the echo trains. For each possible combination of the three parameters (power law, size of the fully sampled part, and FSE scheme), forty schemes were generated, and the acquisition was simulated by selecting the relevant phase lines from fully sampled Multi-Slice-Multi-Echo acquisition of a citrus fruit using a volume quadrature coil (TE=11,5-92 ms, 8 echos, TR=2500ms, Fov=6x6 cm, matrix:256x256). The COMPASS algorithm was used for reconstruction [5] with λ=0.12. To evaluate the image quality the Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index (SSIM) [3] were used, both over the whole image as in a region of interest covering only signal. The fully sampled MSME image at the relevant echo time was used as a reference. A multiple linear regression test was used to estimate the effect of the power law and size of the fully sampled central part of k-space.
The results show that the power of the PDF should be as low as possible, while 50-66% of the total data sampled should be fully sampled. Prime ordering [6] works best when the effective echo time is at the extremes of the echo train, but it is better to order the blocks sequentially for centrally located EET’s. The figure shows the results for a speed up factor of two at EET= central echo location, for the 5 different FSE ordering schemes used.
In conclusion, when the parameters and RARE ordering are carefully chosen, pseudo-random schemes can give images of consistent quality with CS. We believe this relies on the local degree of sparsity in k-space and as such the findings are rather generally usable, in the sense that it matters how your sampling scheme looks for CS. A good image quality with higher speed-up factors depends on trajectories that sample the right regions in k-space.
Acknowledgements
This research was made possible with the help of the ICON project call 2011 “SuperMRI”, and the Interdisciplinary PhD grant (ID) BOF UA 2012 “Optimized workflow for in vivo small animal diffusion weighted MRI studies of white matter diseases: from acquisition to quantification.“
References
[1] E. J. Candès, J. K. Romberg, and T. Tao. (2006). Stable Signal Recovery from Incomplete and Inaccurate Measurements, vol. LIX, pp. 1207–1223
[2] M. Lustig, D. Donoho, J. M. Santos, and J. M. Pauly, (2008). Compressed Sensing MRI, IEEE Signal Processing Magazine, 25(2): 72–82.
[3] M. Lustig, D. Donoho, and J. M. Pauly, (2007). Sparse MRI: The application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine, 58(6): 1182–95.
[4] J. Aelterman, H. Q. Luong, B. Goossens, A. Pizurica, and W. Philips, (2010). COMPASS: A joint framework for Parallel Imaging and Compressive Sensing in MRI, in 2010 IEEE International Conference on Image Processing, pp. 1653–1656.
[5] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, (2004). Image quality assessment: from error visibility to structural similarity, IEEE Trans Image Processing, 13(4): 600–12.
[6] Y. Hitata, M. Sasaki, K. Esashika, and H. Gakumazawa, (2008). Hitachi’s Prime Fast Spin Echo Technology: Efficacies in Improving Image Quality and Usability. Hitachi Medical Systems America Inc.
Keywords:
Fast Spin Echo,
FSE,
compressed sensing,
CS,
trajectories,
k-space sampling,
image quality assessment
Conference:
Imaging the brain at different scales: How to integrate multi-scale structural information?, Antwerp, Belgium, 2 Sep - 6 Sep, 2013.
Presentation Type:
Poster presentation
Topic:
Poster session
Citation:
Naeyaert
M,
Aelterman
J,
Van Audekerke
J and
Verhoye
M
(2013). Quality and Stability of Compressed Sensing Schemes in the Fast Spin Echo Sequence.
Front. Neuroinform.
Conference Abstract:
Imaging the brain at different scales: How to integrate multi-scale structural information?.
doi: 10.3389/conf.fninf.2013.10.00037
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Received:
01 Aug 2013;
Published Online:
31 Aug 2013.
*
Correspondence:
Mr. Maarten Naeyaert, University of Antwerp, Department of Biomedical Sciences, Antwerp, 2100, Belgium, telptilion@gmail.com