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.

A new nonlocal nonlinear diffusion equation for image denoising and data analysis / G. Aletti, M. Moroni, G. Naldi. - (2017 Jul 20).

A new nonlocal nonlinear diffusion equation for image denoising and data analysis

G. Aletti
Primo
;
G. Naldi
Ultimo
2017

Abstract

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.
nonlocal operators; nonlinear diffusion; feature extraction; signal processing
Settore MAT/08 - Analisi Numerica
Settore MAT/06 - Probabilita' e Statistica Matematica
20-lug-2017
http://arxiv.org/abs/1707.06396v1
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/518547
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