ABSTRACT

A new nonlocal total variation reaction–diffusion system is proposed, analysed and implemented for image denoising. In the way, it is obtained by analysing the case where $p\to 1$ in the nonlocal p-Laplacian reaction–diffusion system proposed in [F. Karami, D. Meskine, and K. Sadik, A new nonlocal model for the restoration of textured images, J. Appl. Anal. Comput. 9(6) (2019), pp. 2070–2095.]. We established the existence and uniqueness of the proposed model. Numerical and comparatives experiments are presented that illustrate the main features of the new model and that demonstrate its effectiveness as a denoising tool.

摘要

提出、分析并实现了一种新的非局部全变反应-扩散系统用于图像去噪。方式中，通过分析以下情况得到$磷\to 1$在非局部p -Laplacian反应-扩散体系在[F.提出 Karami、D. Meskine 和 K. Sadik，用于纹理图像恢复的新非局部模型，J. Appl。肛门。计算。9(6) (2019)，第 2070-2095 页。]。我们建立了所提出模型的存在性和唯一性。数值和比较实验展示了新模型的主要特征，并证明了其作为去噪工具的有效性。