2014/08/22 by Hui Zhang, Zhang, Hui, Lizhi Cheng +1 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Image and Signal Denoising Methods #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #math.OC
paper · pdf · doi:10.48550/arxiv.1408.5214
10 pages, 1 figure
arxiv created 2014/08/22 · openalex publication_date 2014/08/22 · arxiv updated 2014/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Box-constrained L1-minimization can perform remarkably better than classical L1-minimization when correction box constraints are available. And also many practical L1-minimization models indeed involve box constraints because they take certain values from some interval. In this paper, we propose an efficient iteration scheme, namely projected shrinkage (ProShrink) algorithm, to solve a class of box-constrained L1-minimization problems. A key contribution in our technique is that a complicated proximal point operator appeared in the deduction can be equivalently simplified into a projected shrinkage operator. Theoretically, we prove that ProShrink enjoys a convergence of both the primal and dual point sequences. On the numerical level, we demonstrate the benefit of adding box constraints via sparse recovery experiments.