## EdgeCS

 swMATH ID: 14134 Software Authors: Guo, Weihong; Yin, Wotao Description: Edge guided reconstruction for compressive imaging. We propose EdgeCS – an edge guided compressive sensing reconstruction approach – to recover images of higher quality from fewer measurements than the current methods. Edges are important image features that are used in various ways in image recovery, analysis, and understanding. In compressive sensing, the sparsity of image edges has been successfully utilized to recover images. However, edge detectors have not been used on compressive sensing measurements to improve the edge recovery and subsequently the image recovery. This motivates us to propose EdgeCS, which alternatively performs edge detection and image reconstruction in a mutually beneficial way. par The edge detector of EdgeCS is designed to faithfully return partial edges from intermediate image reconstructions even though these reconstructions may still have noise and artifacts. For complex-valued images, it incorporates joint sparsity between the real and imaginary components. EdgeCS has been implemented with both isotropic and anisotropic discretizations of total variation and tested on incomplete $$k$$-space (spectral Fourier) samples. It applies to other types of measurements as well. Experimental results on large-scale real/complex-valued phantom and magnetic resonance (MR) images show that EdgeCS is fast and returns high-quality images. For example, it exactly recovers the $$256 imes 256$$ Shepp-Logan phantom from merely 7 radial lines ($$3.03%$$ $$k$$-space), which is impossible for most existing algorithms. It is able to accurately reconstruct a $$512 imes 512$$ MR image with 0.05 white noise from $$20.87%$$ radial samples. On complex-valued MR images, it obtains recoveries with faithful phases, which are important in many medical applications. Each of these tests took around 30 seconds on a standard PC. Finally, the algorithm is GPU friendly. Homepage: http://epubs.siam.org/doi/ref/10.1137/110837309 Keywords: compressive sensing; edge detection; total variation; discrete Fourier transform; magnetic resonance imaging; numerical examples; biomedical imaging; image recovery; image reconstruction Related Software: RecPF; PDCO; DLMRI-Lab; BADMM; Gurobi; PRMLT; BayesDA; CVX; ma2dfc; TFOCS; NESTA; BLOOMP; TwIST; TVAL3; FTVd Referenced in: 12 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Edge guided reconstruction for compressive imaging. Zbl 1259.65102
Guo, Weihong; Yin, Wotao
2012
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### Referenced by 29 Authors

 3 Guo, Weihong 2 Lou, Yifei 1 Churchill, Victor 1 Dong, Hongbo 1 Duan, Yuping 1 Gelb, Anne 1 Gong, Changcheng 1 Han, Bo 1 He, Chuan 1 Hu, Changhua 1 Huang, Ting-Zhu 1 Li, Xuelong 1 Ma, Tian-Hui 1 Osher, Stanley Joel 1 Qin, Jing 1 Rahimi, Yaghoub 1 Schaeffer, Hayden 1 Song, Guohui 1 Tang, Jinping 1 Tong, Shanshan 1 Wang, Chengxiang 1 Xie, Weisi 1 Yan, Mengyuan 1 Yang, Yi 1 Yang, Yufei 1 Yin, Wotao 1 Zeng, Li 1 Zhang, Wei 1 Zhang, Yue
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### Referenced in 8 Serials

 4 SIAM Journal on Imaging Sciences 1 Inverse Problems 1 Information Sciences 1 Journal of Scientific Computing 1 Numerical Algorithms 1 Applied Mathematical Modelling 1 Journal of Mathematical Imaging and Vision 1 SIAM Journal on Scientific Computing
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### Referenced in 11 Fields

 8 Numerical analysis (65-XX) 8 Information and communication theory, circuits (94-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Computer science (68-XX) 5 Operations research, mathematical programming (90-XX) 3 Biology and other natural sciences (92-XX) 2 Statistics (62-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Partial differential equations (35-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Optics, electromagnetic theory (78-XX)