Papers › Theory and Fast Learned Solver for ℓ¹-TV Regularization
Theory and Fast Learned Solver for ℓ¹-TV Regularization
Xinling Liu, Jianjun Wang, Bangti Jin
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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.
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