A new nonlocal nonlinear diffusion equation for image denoising and data analysis
For researchers in image processing, this offers a new denoising method with theoretical guarantees, but the improvement over existing methods is not quantified.
The paper introduces a new nonlinear anisotropic diffusion equation for image denoising that uses a nonlocal diffusivity coefficient based on local bounded variation and oscillatory patterns. Numerical experiments demonstrate the method's effectiveness, though no concrete numerical results are provided.
In this paper we introduce and study a new feature-preserving nonlinear anisotropic diffusion 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 of our nonlinear and nonlocal diffusion equation in the two dimensional case (images processing). Finally, we propose a numerical scheme with some numerical experiments which demonstrate the effectiveness of the new method.