We prove a result on the existence and uniqueness of the solution of a new feature-preserving nonlinear nonlocal diffusion equation for signal denoising for the one-dimensional case. The 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.
A new nonlocal nonlinear diffusion equation: the one-dimensional case / G. Aletti, A. Benfenati, G. Naldi. - In: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 0004-9727. - (2022). [Epub ahead of print] [10.1017/S0004972722000363]
A new nonlocal nonlinear diffusion equation: the one-dimensional case
G. AlettiPrimo
;A. BenfenatiSecondo
;G. Naldi
Ultimo
2022
Abstract
We prove a result on the existence and uniqueness of the solution of a new feature-preserving nonlinear nonlocal diffusion equation for signal denoising for the one-dimensional case. The 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.
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