Color image denoising under mixed multiplicative and Gaussian noise via group-sparse representation and SVTV regularization

Color image denoising under the simultaneous presence of multiplicative and Gaussian noise is challenging due to the differing statistical properties of the two noise types. We propose a variational framework that integrates an infimal-convolution-based data-fidelity term with saturation-value total variation (SVTV) and group-based sparse representation (GSR) regularization. By explicitly decoupling the multiplicative and Gaussian noise components, the data-fidelity term enables effective suppression of mixed noise. The two regularizers play complementary roles: SVTV promotes piecewise-smooth reconstructions while preserving edges, whereas GSR enhances fine details and textures and mitigates the staircase artifacts induced by SVTV. The resulting nonconvex optimization problem is addressed using a proximal alternating minimization strategy, with the alternating direction method of multipliers employed to efficiently solve the subproblems. A convergence analysis of the proposed algorithm is provided. Numerical experiments demonstrate that the proposed method consistently outperforms existing approaches for denoising color images corrupted by mixed multiplicative and Gaussian noise.