Abstract
In recent years, the fractional-order derivative has achieved great success in removing Gaussian noise, impulsive noise, multiplicative noise and so on, but few works have been conducted to remove Cauchy noise. In this paper, we propose a novel nonconvex variational model for removing Cauchy noise based on the truncated fractional-order total variation. The new model can effectively reduce the staircase effect and keep small details or textures while removing Cauchy noise. In order to solve the nonconvex truncated fractional-order total variation regularization model, we propose an efficient alternating minimization method under the framework of the alternating direction multiplier method. Experimental results illustrate the effectiveness of the proposed model, compared to some previous models.
Highlights
Image denoising is the most typical problem in image processing, which aims to recover a clean image from a degraded image with noise
We focus on the problem of Cauchy noise removal in images
This noise is commonly found in wireless communication systems, synthetic aperture radar (SAR) images, and biomedical images [1,2,3,4]
Summary
Image denoising is the most typical problem in image processing, which aims to recover a clean image from a degraded image with noise. Some fractional-order total variation regularization models [19,20,21] have been proposed for additive and multiplicative noise removal. We extend the truncated fractional-order total variation regularization to recover Cauchy noise and propose the following model:. To one that uses the truncated fractional-order total variation regularizer for Cauchy noise removal. This seems to be a simple generalization, its optimization is more challenging than Gaussian denoising due to the nonconvexity of the data fidelity term. The main contributions of our work are as follows: (1) We propose a novel minimization model for Cauchy noise removal by adopting the truncated fractional-order total variation regularization.
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