Comparative study of non-convex penalties and related algorithms in compressed sensing

Non-convex penalties are widely used in sparse representation models and fields such as compressed sensing, because they can efficiently recover signals with a high sparsity level compared with the well-known ℓ1-norm. However, few classic penalties have been selected in most applications without exp...

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Veröffentlicht in:Digital signal processing Jg. 135; S. 103937
Hauptverfasser: Xu, Fanding, Duan, Junbo, Liu, Wenyu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 30.04.2023
Schlagworte:
Compressed sensing
Difference of convex functions
Iterative thresholding
Non-convex penalty
Sparse representation
Difference of convex functions
Sparse representation
Iterative thresholding
Compressed sensing
Non-convex penalty
ISSN:1051-2004, 1095-4333
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Zusammenfassung:Non-convex penalties are widely used in sparse representation models and fields such as compressed sensing, because they can efficiently recover signals with a high sparsity level compared with the well-known ℓ1-norm. However, few classic penalties have been selected in most applications without exploring the performance of other non-convex penalties. Therefore, the objective of this study is to provide a comparative and comprehensive study on non-convex penalties. We first collected nine representative non-convex penalties and then applied two optimization frameworks: the difference of convex function algorithm (DCA) and iterative shrinkage/thresholding algorithm (ISTA) to solve the optimization problems associated with the nine non-convex penalties. The performances of the nine penalties and two algorithms were systematically compared and analyzed experimentally. We hope that these results that concern non-convex penalty selection in sparse representation models can be used as a general reference for research. •The performance of nine representative non-convex penalties were comprehensively compared.•The thresholding functions of penalties of the iterative shrinkage/thresholding algorithm (ISTA) were explicitly presented.•The solution paths of all penalties were demonstrated.
ISSN:1051-2004
1095-4333
DOI:10.1016/j.dsp.2023.103937