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
A New Nonlocal Nonlinear Diffusion Equation for Data Analysis / G. Aletti, M. Moroni, G. Naldi. - In: ACTA APPLICANDAE MATHEMATICAE. - ISSN 0167-8019. - (2019). [Epub ahead of print]
A New Nonlocal Nonlinear Diffusion Equation for Data Analysis
Aletti, Giacomo;Naldi, Giovanni
2020-08
Abstract
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 approachFile | Dimensione | Formato | |
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