A new nonlocal nonlinear diffusion of image processing

DOI10.1016/j.jde.2009.03.017zbMath1170.35450OpenAlexW1972397486MaRDI QIDQ1022946

Patrick Guidotti

Publication date: 10 June 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.03.017

zbMATH Keywords

fractional derivativeswell-posednessperiodic boundary conditionsPerona-Malik equationnoise reductionnontrivial equilibria

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Nonlinear parabolic equations (35K55) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Periodic solutions to PDEs (35B10)

Related Items (16)

A Total Fractional-Order Variation Model for Image Restoration with Nonhomogeneous Boundary Conditions and Its Numerical Solution ⋮ PASSING TO THE LIMIT IN MAXIMAL SLOPE CURVES: FROM A REGULARIZED PERONA–MALIK EQUATION TO THE TOTAL VARIATION FLOW ⋮ A non-local diffusion equation for noise removal ⋮ Variational image registration by a total fractional-order variation model ⋮ Two enhanced fourth order diffusion models for image denoising ⋮ A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona-Malik functional ⋮ A denoising model based on the fractional Beltrami regularization and its numerical solution ⋮ Monotonicity Properties of Limits of Solutions to the Semidiscrete Scheme for a Class of Perona–Malik Type Equations ⋮ Simultaneous denoising and enhancement of signals by a fractal conservation law ⋮ Well-posedness for a class of fourth order diffusions for image processing ⋮ A backward-forward regularization of the Perona-Malik equation ⋮ On a system of adaptive coupled PDEs for image restoration ⋮ Nonlinear fractional diffusion model for deblurring images with textures ⋮ Weighted and well-balanced anisotropic diffusion scheme for image denoising and restoration ⋮ Well-posedness of a nonlocal nonlinear diffusion equation of image processing ⋮ An Example of Global Classical Solution for the Perona-Malik Equation

Cites Work

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• The $\Gamma $-limit and the related gradient flow for singular perturbation functionals of Perona-Malik type
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