ADMM algorithm for some regularized Perona-Malik equation and applications to image denoising

In this paper, we propose a new approach for solving the proposed variational model derived from Perona-Malik (PM) equation. This problem is the combination of P-M model and p-Laplacian operator. Our approach exploiting the different values of p (p near 1 or infinity) and using a variable contrast parameter. to adaptively control the scattering pattern in the restored image. Firstly, we present the variational model, and we prove the existence and uniqueness of the minimizer. To solve numerically our problem, we apply theADMMmethod to derive a robust scheme. Finally, we illustrate the effectiveness of our algorithm with various numerical tests which can compare favorably with some existing methods in the literature.

Automated summary

In this paper, a new approach is proposed for solving the variational model derived from the Perona-Malik equation, which can be used to control the scattering pattern in the restored image and demonstrates favorable performance in numerical tests.