Abstract
In this paper, we focus on a numerical method of a problem called the Perona-Malik inequality which we use for image denoising. This model is obtained as the limit of the Perona-Malik model and the p-Laplacian operator with p→∞. In Atlas et al., (Nonlinear Anal. Real World Appl 18:57–68, 2014), the authors have proved the existence and uniqueness of the solution of the proposed model. However, in their work, they used the explicit numerical scheme for approximated problem which is strongly dependent to the parameter p. To overcome this, we use in this work an efficient algorithm which is a combination of the classical additive operator splitting and a nonlinear relaxation algorithm. At last, we have presented the experimental results in image filtering show, which demonstrate the efficiency and effectiveness of our algorithm and finally, we have compared it with the previous scheme presented in Atlas et al., (Nonlinear Anal. Real World Appl 18:57–68, 2014).
Highlights
Image denoising is one of the fundamental challenges in the field of image processing and computer vision
Partial differential equations [1,2,3,4,5,6,7], variational models [8,9,10,11], energy minimization, bilateral filtering [12, 13], and wavelet thresholding [14, 15] have been proposed depending on the domain of applications
The numerical simulations produce a phenomenon known as the staircase effect, which causes images to look blocky
Summary
Image denoising is one of the fundamental challenges in the field of image processing and computer vision. The aim is to remove noise while preserving edges, boundaries, and textures To handle this problem, partial differential equations [1,2,3,4,5,6,7], variational models [8,9,10,11], energy minimization, bilateral filtering [12, 13], and wavelet thresholding [14, 15] have been proposed depending on the domain of applications. In 1990, Perona-Malik [2] proposed a nonlinear diffusion equation that succeeded in image denoising This model is an ill-posed problem in analytical point of view, besides, the numerical simulations produce the staircase effect. Some numerical simulations are given to demonstrate the effectiveness of the proposed algorithm
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