2015/12/31 by Peijun Chen, Chen, Peijun, Jianguo Huang +3 · 1 citation
Engineering · Mathematics · #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques #math.OC
paper · pdf · doi:10.48550/arxiv.1512.09235
17 pages, 8 figures
arxiv created 2015/12/31 · openalex publication_date 2015/12/31 · arxiv updated 2016/01/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Many problems arising in image processing and signal recovery with multi-regularization can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function and a nonsmooth function. In this paper, we propose a primal-dual fixed-point (PDFP) scheme to solve the above class of problems. The proposed algorithm for three block problems is a fully splitting symmetric scheme, only involving explicit gradient and linear operators without inner iteration, when the nonsmooth functions can be easily solved via their proximity operators, such as ℓ1 type regularization. We study the convergence of the proposed algorithm and illustrate its efficiency through examples on fused LASSO and image restoration with non-negative constraint and sparse regularization.