A new approach for Cauchy noise removal

Lufeng Bai; Lufeng Bai

doi:10.3934/math.2021596

AIMS Mathematics

2021, Volume 6, Issue 9: 10296-10312. doi: 10.3934/math.2021596

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A new approach for Cauchy noise removal

Lufeng Bai ^,

Jiangsu Second Normal University, Nanjing 210013, China

Received: 13 April 2021 Accepted: 25 June 2021 Published: 13 July 2021
MSC : 49M20, 49N45, 65K10, 90C90

In this paper, a new total generalized variational (TGV) model for restoring images with Cauchy noise is proposed, which contains a non-convex fidelity term and a TGV regularization term. In order to obtain a strictly convex model, we add an appropriate proximal term to the non-convex fidelity term. We prove that the solution of the proposed model exists and is unique. Due to the convexity of the proposed model and in order to get a convergent algorithm, we employ an alternating minimization algorithm to solve the proposed model. Finally, we demonstrate the performance of our scheme by numerical examples. Numerical results demonstrate that the proposed algorithm significantly outperforms some previous methods for Cauchy noise removal.
- Cauchy noise,
- TGV,
- convergence,
- alternating minimization,
- non-expansive
Citation: Lufeng Bai. A new approach for Cauchy noise removal[J]. AIMS Mathematics, 2021, 6(9): 10296-10312. doi: 10.3934/math.2021596

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Abstract

In this paper, a new total generalized variational (TGV) model for restoring images with Cauchy noise is proposed, which contains a non-convex fidelity term and a TGV regularization term. In order to obtain a strictly convex model, we add an appropriate proximal term to the non-convex fidelity term. We prove that the solution of the proposed model exists and is unique. Due to the convexity of the proposed model and in order to get a convergent algorithm, we employ an alternating minimization algorithm to solve the proposed model. Finally, we demonstrate the performance of our scheme by numerical examples. Numerical results demonstrate that the proposed algorithm significantly outperforms some previous methods for Cauchy noise removal.

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