A symmetric alternating minimization algorithm for total variation minimization

2020/02/21 by Lei Yuan, Jiaxin Xie, Lei, Yuan +1
Engineering · Mathematics · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2002.09180

openalex publication_date 2020/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose a novel symmetric alternating minimization algorithm to solve a broad class of total variation (TV) regularization problems. Unlike the usual z^k→ x^k Gauss-Seidel cycle, the proposed algorithm performs the special x^k→ z^k→ x^k cycle. The main idea for our setting is the recent symmetric Gauss-Seidel (sGS) technique which is developed for solving the multi-block convex composite problem. This idea also enables us to build the equivalence between the proposed method and the well-known accelerated proximal gradient (APG) method. The faster convergence rate of the proposed algorithm can be directly obtained from the APG framework and numerical results including image denoising, image deblurring, and analysis sparse recovery problem demonstrate the effectiveness of the new algorithm.

Citations

• On the Convergence of the Lagged Diffusivity Fixed Point Method in Total Variation Image Restoration
• Fast Image Recovery Using Variable Splitting and Constrained Optimization

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