2024/12/04 by Xinling Liu, Jianjun Wang, Liu, Xinling +3
Mathematics · Engineering · Computer Science · #Numerical methods in inverse problems #Electrical and Bioimpedance Tomography #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.2412.03269
The ℓ1 and total variation (TV) penalties have been used successfully in many areas, and the combination of the ℓ1 and TV penalties can lead to further improved performance. In this work, we investigate the mathematical theory and numerical algorithms for the ℓ1-TV model in the context of signal recovery: we derive the sample complexity of the ℓ1-TV model for recovering signals with sparsity and gradient sparsity. Also we propose a novel algorithm (PGM-ISTA) for the regularized ℓ1-TV problem, and establish its global convergence and parameter selection criteria. Furthermore, we construct a fast learned solver (LPGM-ISTA) by unrolling PGM-ISTA. The results for the experiment on ECG signals show the superior performance of LPGM-ISTA in terms of recovery accuracy and computational efficiency.