An Efficient Inexact Gauss–Seidel-Based Algorithm for Image Restoration with Mixed Noise

• Published in: Journal of scientific computing 2024-05, Vol.99 (2), p.54, Article 54
• Main Authors: Wu, Tingting, Min, Yue, Huang, Chaoyan, Li, Zhi, Wu, Zhongming, Zeng, Tieyong
• Format: Article
• Language: English
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Convexity; Deep learning; Image restoration; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical models; Mathematics; Mathematics and Statistics; Numerical analysis; Numerical methods; Regularization; Regularization methods; Theoretical
• ISSN: 0885-7474; 1573-7691
• DOI: 10.1007/s10915-024-02510-8

A challenge in image restoration is to recover a clear image from the blurry observation in the presence of different types of noise. There are few works addressing image deblurring under mixed noise. To handle this issue, we propose a general model based on classical wavelet tight frame regularization. We utilize a convexity-preserving term to obtain a component-wise convex model under a mild condition. Indeed, to reduce the cost of solving subproblems, the inexact Gauss–Seidel-based majorized semi-proximal alternating direction method of multipliers (sGS-imsPADMM) with relative error control is developed. Besides, the global convergence of sGS-imsPADMM is demonstrated. Numerical results for the image restoration problems show that the proposed model and solving approach are superior to some state-of-the-art methods both in numerical analysis and visual quality.