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
A recent study conducted REF in image denoising problem, proved that a combination of classical additive operator splitting and a nonlinear relaxation algorithm are able to produce an accurate image restoration which is also able to control the problem of stability.
A splitting algorithm for a novel regularization of Perona-Malik and application to image restoration
EURASIP Journal on Advances in Signal Processing
Computer Science