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Group-Based Sparse Representation Based on <em>l</em>p-norm Minimization for Compressive Sensing

Ruijing Li, Yechao Bai, Xinggan Zhang, Lan Tang, and Qiong Wang
School of Electronic Science and Engineering, Nanjing University, Nanjing, China
Abstract—Sparse coding has been applied in various domains, especially in image restoration. Most methods depend on the l1-norm optimization techniques and the patch-based sparse representation models, but they suffer from two limits: one is the high computational complexity in dictionary learning; the other is ignoring the relationship among patches which influences the accuracy of sparse coding coefficients. In this paper, we choose the group-based sparse representation models to simple calculation process and realize the nonlocal self-similarity of images by graph-based transform dictionary design. Besides, we utilize lp-norm minimization to solve nonconvex optimization problems on the basis of the weighted schatten p-norm minimization, which can make the optimization model more flexible. Through reasonable parameters selection, experimental results show that our proposed method has a better performance on the compressive sensing than many current state-of-the-art schemes in both peak signal-to-noise ratio and visual perception. 

Index Terms—sparse coding, group-based sparse, lp-norm minimization, compressive sensing

Cite: Ruijing Li, Yechao Bai, Xinggan Zhang, Lan Tang, and Qiong Wang, "Group-Based Sparse Representation Based on lp-norm Minimization for Compressive Sensing," International Journal of Signal Processing Systems, Vol. 8, No. 1, pp. 13-18, March 2020. doi: 10.18178/ijsps.8.1.13-18

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