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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2501.15221 |
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| _version_ | 1866917903211692032 |
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| author | Huang, Meng Li, Shidong |
| author_facet | Huang, Meng Li, Shidong |
| contents | Recovery error bounds of tail-minimization and the rate of convergence of an efficient proximal alternating algorithm for sparse signal recovery are considered in this article. Tail-minimization focuses on minimizing the energy in the complement $T^c$ of an estimated support $T$. Under the restricted isometry property (RIP) condition, we prove that tail-$\ell_1$ minimization can exactly recover sparse signals in the noiseless case for a given $T$. In the noisy case, two recovery results for the tail-$\ell_1$ minimization and the tail-lasso models are established. Error bounds are improved over existing results. Additionally, we show that the RIP condition becomes surprisingly relaxed, allowing the RIP constant to approach $1$ as the estimation $T$ closely approximates the true support $S$. Finally, an efficient proximal alternating minimization algorithm is introduced for solving the tail-lasso problem using Hadamard product parametrization. The linear rate of convergence is established using the Kurdyka-Łojasiewicz inequality. Numerical results demonstrate that the proposed algorithm significantly improves signal recovery performance compared to state-of-the-art techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Performance analysis of tail-minimization and the linear rate of convergence of a proximal algorithm for sparse signal recovery Huang, Meng Li, Shidong Information Theory Recovery error bounds of tail-minimization and the rate of convergence of an efficient proximal alternating algorithm for sparse signal recovery are considered in this article. Tail-minimization focuses on minimizing the energy in the complement $T^c$ of an estimated support $T$. Under the restricted isometry property (RIP) condition, we prove that tail-$\ell_1$ minimization can exactly recover sparse signals in the noiseless case for a given $T$. In the noisy case, two recovery results for the tail-$\ell_1$ minimization and the tail-lasso models are established. Error bounds are improved over existing results. Additionally, we show that the RIP condition becomes surprisingly relaxed, allowing the RIP constant to approach $1$ as the estimation $T$ closely approximates the true support $S$. Finally, an efficient proximal alternating minimization algorithm is introduced for solving the tail-lasso problem using Hadamard product parametrization. The linear rate of convergence is established using the Kurdyka-Łojasiewicz inequality. Numerical results demonstrate that the proposed algorithm significantly improves signal recovery performance compared to state-of-the-art techniques. |
| title | Performance analysis of tail-minimization and the linear rate of convergence of a proximal algorithm for sparse signal recovery |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.15221 |