On a System of Adaptive Coupled PDEs for Image Restoration

Authors:
V. B. Prasath;D. Vorotnikov
Affiliations:
Department of Computer Science, University of Missouri-Columbia, Columbia, USA 65211;CMUC, Department of Mathematics, University of Coimbra, Coimbra, Portugal 3001-454
Venue:
Journal of Mathematical Imaging and Vision
Year:
2014

Citing 41
Cited 0

A Computational Approach to Edge Detection

IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion

IEEE Transactions on Pattern Analysis and Machine Intelligence
Feature-oriented image enhancement using shock filters

SIAM Journal on Numerical Analysis
Biased anisotropic diffusion: a unified regularization and diffusion approach to edge detection

Image and Vision Computing - Special issue on the first ECCV 1990
Image selective smoothing and edge detection by nonlinear diffusion

SIAM Journal on Numerical Analysis
Nonlinear Image Filtering with Edge and Corner Enhancement

IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear total variation based noise removal algorithms

Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Signal and image restoration using shock filters and anisotropic diffusion

SIAM Journal on Numerical Analysis
Image Sequence Analysis via Partial Differential Equations

Journal of Mathematical Imaging and Vision
Analytic results related to magneto-hydrodynamic turbulence

Physica D
Vector Median Filters, Inf-Sup Operations, and Coupled PDE's: Theoretical Connections

Journal of Mathematical Imaging and Vision
Smoothing and edge detection by time-varying coupled nonlinear diffusion equations

Computer Vision and Image Understanding
On the Incorporation of Time-delay Regularization into Curvature-based Diffusion

Journal of Mathematical Imaging and Vision
Diffusions and Confusions in Signal and Image Processing

Journal of Mathematical Imaging and Vision
High-Order Total Variation-Based Image Restoration

SIAM Journal on Scientific Computing
Total variation image restoration: numerical methods and extensions

ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 3 - Volume 3
Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional

International Journal of Computer Vision
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection

International Journal of Computer Vision
Coupled anisotropic diffusion for image selective smoothing

Signal Processing
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)

Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
A Finite Markov Random Field approach to fast edge-preserving image recovery

Image and Vision Computing
Image restoration combining a total variational filter and a fourth-order filter

Journal of Visual Communication and Image Representation
An Improved Hybrid Model for Molecular Image Denoising

Journal of Mathematical Imaging and Vision
A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors

IEEE Transactions on Pattern Analysis and Machine Intelligence
Two new nonlinear nonlocal diffusions for noise reduction

Journal of Mathematical Imaging and Vision
Mumford-Shah regularizer with contextual feedback

Journal of Mathematical Imaging and Vision
Properties of Higher Order Nonlinear Diffusion Filtering

Journal of Mathematical Imaging and Vision
The Split Bregman Method for L1-Regularized Problems

SIAM Journal on Imaging Sciences
Generalised Nonlocal Image Smoothing

International Journal of Computer Vision
Automated Regularization Parameter Selection in Multi-Scale Total Variation Models for Image Restoration

Journal of Mathematical Imaging and Vision
Two Enhanced Fourth Order Diffusion Models for Image Denoising

Journal of Mathematical Imaging and Vision
Fully fractional anisotropic diffusion for image denoising

Mathematical and Computer Modelling: An International Journal
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images

IEEE Transactions on Pattern Analysis and Machine Intelligence
Deterministic edge-preserving regularization in computed imaging

IEEE Transactions on Image Processing
A Volterra type model for image processing

IEEE Transactions on Image Processing
Variational approach for edge-preserving regularization using coupled PDEs

IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering

IEEE Transactions on Image Processing
Fourth-order partial differential equations for noise removal

IEEE Transactions on Image Processing
Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time

IEEE Transactions on Image Processing
Image quality assessment: from error visibility to structural similarity

IEEE Transactions on Image Processing
Variational denoising of partly textured images by spatially varying constraints

IEEE Transactions on Image Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we consider a coupled system of partial differential equations (PDEs) based model for image restoration. Both the image and the edge variables are incorporated by coupling them into two different PDEs. It is shown that the initial-boundary value problem has global in time dissipative solutions (in a sense going back to P.-L. Lions), and several properties of these solutions are established. Some numerical examples are given to highlight the denoising nature of the proposed model along with some comparison results.