A variational image denoising model under mixed Cauchy and Gaussian noise

Miyoun Jung; Miyoun Jung

doi:10.3934/math.20221080

AIMS Mathematics

2022, Volume 7, Issue 11: 19696-19726. doi: 10.3934/math.20221080

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Research article

A variational image denoising model under mixed Cauchy and Gaussian noise

Miyoun Jung ^,

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

Received: 23 June 2022 Revised: 11 August 2022 Accepted: 22 August 2022 Published: 06 September 2022
MSC : 68U10, 65K10, 94A08, 49J40

In this article, we propose a novel variational model for restoring images in the presence of the mixture of Cauchy and Gaussian noise. The model involves a novel data-fidelity term that features the mixed noise as an infimal convolution of two noise distributions and total variation regularization. This data-fidelity term contributes to suitable separation of Cauchy noise and Gaussian noise components, facilitating simultaneous removal of the mixed noise. Besides, the total variation regularization enables adequate denoising in homogeneous regions while conserving edges. Despite the nonconvexity of the model, the existence of a solution is proven. By employing an alternating minimization approach and the alternating direction method of multipliers, we present an iterative algorithm for solving the proposed model. Experimental results validate the effectiveness of the proposed model compared to other existing models according to both visual quality and some image quality measurements.
- image denoising,
- mixed Cauchy-Gaussian noise,
- variational model,
- infimal convolution,
- total variation
Citation: Miyoun Jung. A variational image denoising model under mixed Cauchy and Gaussian noise[J]. AIMS Mathematics, 2022, 7(11): 19696-19726. doi: 10.3934/math.20221080

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Abstract

In this article, we propose a novel variational model for restoring images in the presence of the mixture of Cauchy and Gaussian noise. The model involves a novel data-fidelity term that features the mixed noise as an infimal convolution of two noise distributions and total variation regularization. This data-fidelity term contributes to suitable separation of Cauchy noise and Gaussian noise components, facilitating simultaneous removal of the mixed noise. Besides, the total variation regularization enables adequate denoising in homogeneous regions while conserving edges. Despite the nonconvexity of the model, the existence of a solution is proven. By employing an alternating minimization approach and the alternating direction method of multipliers, we present an iterative algorithm for solving the proposed model. Experimental results validate the effectiveness of the proposed model compared to other existing models according to both visual quality and some image quality measurements.

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