Group sparse representation and saturation-value total variation based color image denoising under multiplicative noise

Miyoun Jung; Miyoun Jung

doi:10.3934/math.2024294

AIMS Mathematics

2024, Volume 9, Issue 3: 6013-6040. doi: 10.3934/math.2024294

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Research article

Group sparse representation and saturation-value total variation based color image denoising under multiplicative noise

Miyoun Jung ^,

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

Received: 23 November 2023 Revised: 19 January 2024 Accepted: 26 January 2024 Published: 01 February 2024
MSC : 68U10, 65K10, 94A08, 49J40

In this article, we propose a novel group-based sparse representation (GSR) model for restoring color images in the presence of multiplicative noise. This model consists of a convex data-fidelity term, and two regularizations including GSR and saturation-value-based total variation (SVTV). The data-fidelity term is suitable for handling heavy multiplicative noise. GSR enables the retention of textures and details while sufficiently removing noise in smooth regions without producing the staircase artifacts engendered by total variation-based models. Furthermore, we introduce a multi-color channel-based GSR that involves coupling between three color channels. This avoids the generation of color artifacts caused by decoupled color channel-based methods. SVTV further improves the visual quality of restored images by diminishing certain artifacts induced by patch-based methods. To solve the proposed nonconvex model and its subproblem, we exploit the alternating direction method of multipliers, which contributes to an efficient iterative algorithm. Numerical results demonstrate the outstanding performance of the proposed model compared to other existing models regarding visual aspect and image quality evaluation values.
Citation: Miyoun Jung. Group sparse representation and saturation-value total variation based color image denoising under multiplicative noise[J]. AIMS Mathematics, 2024, 9(3): 6013-6040. doi: 10.3934/math.2024294

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Abstract

In this article, we propose a novel group-based sparse representation (GSR) model for restoring color images in the presence of multiplicative noise. This model consists of a convex data-fidelity term, and two regularizations including GSR and saturation-value-based total variation (SVTV). The data-fidelity term is suitable for handling heavy multiplicative noise. GSR enables the retention of textures and details while sufficiently removing noise in smooth regions without producing the staircase artifacts engendered by total variation-based models. Furthermore, we introduce a multi-color channel-based GSR that involves coupling between three color channels. This avoids the generation of color artifacts caused by decoupled color channel-based methods. SVTV further improves the visual quality of restored images by diminishing certain artifacts induced by patch-based methods. To solve the proposed nonconvex model and its subproblem, we exploit the alternating direction method of multipliers, which contributes to an efficient iterative algorithm. Numerical results demonstrate the outstanding performance of the proposed model compared to other existing models regarding visual aspect and image quality evaluation values.

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