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 approach
Nonlinear diffusion; Nonlocal operators; Signal processing
Settore MAT/08 - Analisi Numerica
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
18-lug-2019
ACTA APPLICANDAE MATHEMATICAE
Centro di Ricerca Interdisciplinare su Modellistica Matematica, Analisi Statistica e Simulazione Computazionale per la Innovazione Scientifica e Tecnologica ADAMSS
http://hdl.handle.net/2434/518547
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/661452
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