In this paper we introduce and study a new feature-preserving nonlinear nonlocal diffusion equation for denoising signals. The proposed partial differential equation is based on a novel diffusivity coefficient that uses a nonlocal automatically detected parameter related to the local bounded variation and the local oscillating pattern of the noisy input signal. We provide a mathematical analysis of the existence of the solution in the two dimensional case, but easily extensible to the one-dimensional model. Finally, we show some numerical experiments, which demonstrate the effectiveness of the new approach.

中文翻译：

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用于数据分析的新的非局部非线性扩散方程

在本文中，我们介绍并研究了一种用于信号降噪的新的保留特征的非线性非局部扩散方程。所提出的偏微分方程基于一种新颖的扩散系数，该系数使用与噪声输入信号的局部有界变化和局部振荡模式相关的非局部自动检测参数。我们提供了在二维情况下解决方案存在性的数学分析，但是很容易扩展到一维模型。最后，我们展示了一些数值实验，证明了这种新方法的有效性。