High-order anisotropic diffusion operators in spaces of variable exponents and application to image inpainting and restoration problems
type: Item
instance of: scholarly article
title: High-order anisotropic diffusion operators in spaces of variable exponents and application to image inpainting and restoration problems
zbMATH Open document ID: 1414.65030
author: Anis Theljani
author: Z. Belhachmi
author: M. Moakher
published in: Nonlinear Analysis. Real World Applications
publication date: 2019-02-27T00:00:00Z
review text: The authors consider a class of nonstandard high-order PDEs (partial differential equations), based on the $p(\cdot)$-Laplace operator with variable exponents, for image denoising and image inpainting problems. These equations are obtained from the minimization of a family of anisotropic energies that range between the so-called $T V - H^{- 1}$ and the biharmonic models. The PDE system consists of quasi-linear equations in which fixed point iterative methods are usually used to solve and to prove the convergence of the iterative process. To solve the problems, an algorithm which includes a practical and efficient adaptive strategy for the choice of the exponent $1 < p \leq 2$ is considered. Several numerical examples are presented to test the following approach and to make some comparisons with existing methods.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65N21
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 68U10
zbMATH DE Number: 7030182
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: high-order PDEs
zbMATH Keywords: fixed point method
zbMATH Keywords: anisotropic diffusion
zbMATH Keywords: finite elements
zbMATH Keywords: image inpainting/restoration
zbMATH Keywords: inverse problems
describes a project that uses: FreeFem++
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2018.10.013
OpenAlex ID: W2903540955
cites work: On a Linear Programming Approach to the Discrete Willmore Boundary Value Problem and Generalizations
cites work: Q2957210
cites work: Analysis of a Two-Scale Cahn–Hilliard Model for Binary Image Inpainting
cites work: Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images
cites work: Mathematical models for local nontexture inpaintings
cites work: Digital inpainting based on the Mumford–Shah–Euler image model
cites work: Euler's Elastica and Curvature-Based Inpainting
cites work: A multiscale fourth‐order model for the image inpainting and low‐dimensional sets recovery
cites work: Proximity algorithms for the L1/TV image denoising model
cites work: An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise
cites work: Image Decomposition and Restoration Using Total Variation Minimization and theH1
cites work: Image restoration with a new class of forward-backward-forward diffusion equations of Perona-Malik type with applications to satellite image enhancement
cites work: Two enhanced fourth order diffusion models for image denoising
cites work: A family of nonlinear diffusions connecting Perona-Malik to standard diffusion
cites work: New diffusion models in image processing
cites work: Image recovery via total variation minimization and related problems
cites work: Variable Exponent, Linear Growth Functionals in Image Restoration
cites work: Graduated adaptive image denoising: Local compromise between total variation and isotropic diffusion
cites work: Multiscale Tikhonov-Total Variation Image Restoration Using Spatially Varying Edge Coherence Exponent
cites work: Lebesgue and Sobolev spaces with variable exponents
cites work: On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
cites work: Q3994744
cites work: Variable exponent functionals in image restoration
cites work: Q4792091
cites work: Inverse coefficient problems for monotone potential operators
cites work: The Cauchy problem for a nonlinear elliptic equation: Nash-game approach and application to image inpainting
cites work: Unconditionally stable schemes for higher order inpainting
cites work: Q4399897
cites work: New development in freefem++
cites work: An adaptive approach for the segmentation and the TV-filtering in the optic flow estimation
cites work: Q4877331
Wikidata QID: Q128888170
DOI: 10.1016/J.NONRWA.2018.10.013
Recommended article: High-order discretization of backward anisotropic diffusion and application to image processing
Recommended article: Q4627338
Recommended article: An anisotropic PDE model for image inpainting
Recommended article: Rigorous mathematical investigation of a nonlinear anisotropic diffusion-based image restoration model
Recommended article: Fourth-Order Anisotropic Diffusion for Inpainting and Image Compression
Recommended article: Q3104130
Recommended article: Q4986462
Recommended article: A fast explicit diffusion algorithm of fractional order anisotropic diffusion for image denoising
Recommended article: Partial Differential Equation Methods for Image Inpainting
description: scientific article; zbMATH DE number 7030182