Color image restoration based on saturation-value total variation plus L1 fidelity* *Wang is supported by Natural Science Foundation of Shanghai (18ZR1441800, 22ZR1465300) and the Fundamental Research Funds for the Central Universities.

Abstract

Color image restoration is one of the most important tasks in image processing. In this paper, we propose and develop a novel saturation-value total variation (SVTV) plus L1 fidelity (SVTV-L1) model for color image restoration. SVTV is incorporated in the proposed model for regularizing the objective color image, meanwhile, L1 norm is considered for data fitting term in the proposed energy functional. Theoretically, we investigate the properties of the objective functional and the objective model. Note that the proposed energy functional including L1 norm is nonsmooth. We develop a smooth approximation approach to study the existence and properties of the solution of the proposed optimization problem. Numerically, Poisson noise and mixed noise have been tested and studied in the experimental results. We formulate an effective and efficient algorithm to solve the proposed minimization problem based on the framework of alternating direction method of multipliers. Numerical examples are presented to demonstrate that the performance of the proposed SVTV-L1 model is better than that of other testing methods in terms of visual quality, peak signal-to-noise ratio, and structure similarity.