2025/01/25 by Meng Huang, Huang, Meng, Shidong Li +1
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2501.15221
openalex publication_date 2025/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Tc of an estimated support T. Under the restricted isometry property (RIP) condition, we prove that tail-ℓ1 minimization can exactly recover sparse signals in the noiseless case for a given T. In the noisy case, two recovery results for the tail-ℓ1 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.