1. A New Nonlocal Nonlinear Diffusion Equation for Data Analysis.
- Author
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Aletti, Giacomo, Moroni, Monica, and Naldi, Giovanni
- Subjects
- *
BURGERS' equation , *PARTIAL differential equations , *DATA analysis , *MATHEMATICAL analysis , *SIGNAL denoising - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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