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

Miyoun Jung; Miyoun Jung

doi:10.3934/math.2026158

AIMS Mathematics

2026, Volume 11, Issue 2: 3920-3956. doi: 10.3934/math.2026158

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Research article

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

Miyoun Jung ^,

Department of Mathematics, Hankuk University of Foreign Studies, Yongin 17035, Korea

Received: 17 December 2025 Revised: 29 January 2026 Accepted: 04 February 2026 Published: 09 February 2026
MSC : 68U10, 65K10, 94A08, 65F22, 52A41, 90C26

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.
- color image denoising,
- multiplicative noise,
- Gaussian noise,
- group-based sparse representation,
- saturation-value total variation,
- proximal alternating minimization algorithm
Citation: Miyoun Jung. Color image denoising under mixed multiplicative and Gaussian noise via group-sparse representation and SVTV regularization[J]. AIMS Mathematics, 2026, 11(2): 3920-3956. doi: 10.3934/math.2026158

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Abstract

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.

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