Signal and Image Recovery with Scale and Signed Permutation Invariant Sparsity-Promoting Functions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918191972745216 |
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| author | Jia, Jianqing Prater-Bennette, Ashley Shen, Lixin |
| author_facet | Jia, Jianqing Prater-Bennette, Ashley Shen, Lixin |
| contents | Sparse signal recovery has been a cornerstone of advancements in data processing and imaging. Recently, the squared ratio of $\ell_1$ to $\ell_2$ norms, $(\ell_1/\ell_2)^2$, has been introduced as a sparsity-prompting function, showing superior performance compared to traditional $\ell_1$ minimization, particularly in challenging scenarios with high coherence and dynamic range. This paper explores the integration of the proximity operator of $(\ell_1/\ell_2)^2$ and $\ell_1/\ell_2$ into efficient optimization frameworks, including the Accelerated Proximal Gradient (APG) and Alternating Direction Method of Multipliers (ADMM). We rigorously analyze the convergence properties of these algorithms and demonstrate their effectiveness in compressed sensing and image restoration applications. Numerical experiments highlight the advantages of our proposed methods in terms of recovery accuracy and computational efficiency, particularly under noise and high-coherence conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05777 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Signal and Image Recovery with Scale and Signed Permutation Invariant Sparsity-Promoting Functions Jia, Jianqing Prater-Bennette, Ashley Shen, Lixin Optimization and Control Signal Processing Sparse signal recovery has been a cornerstone of advancements in data processing and imaging. Recently, the squared ratio of $\ell_1$ to $\ell_2$ norms, $(\ell_1/\ell_2)^2$, has been introduced as a sparsity-prompting function, showing superior performance compared to traditional $\ell_1$ minimization, particularly in challenging scenarios with high coherence and dynamic range. This paper explores the integration of the proximity operator of $(\ell_1/\ell_2)^2$ and $\ell_1/\ell_2$ into efficient optimization frameworks, including the Accelerated Proximal Gradient (APG) and Alternating Direction Method of Multipliers (ADMM). We rigorously analyze the convergence properties of these algorithms and demonstrate their effectiveness in compressed sensing and image restoration applications. Numerical experiments highlight the advantages of our proposed methods in terms of recovery accuracy and computational efficiency, particularly under noise and high-coherence conditions. |
| title | Signal and Image Recovery with Scale and Signed Permutation Invariant Sparsity-Promoting Functions |
| topic | Optimization and Control Signal Processing |
| url | https://arxiv.org/abs/2511.05777 |