A class of quasi-variational inequalities for adaptive image denoising and decomposition

Authors:
Frank Lenzen;Florian Becker;Jan Lellmann;Stefania Petra;Christoph Schnörr
Affiliations:
Heidelberg Collaboratory for Image Processing & Image and Pattern Analysis Group, University of Heidelberg, Heidelberg, Germany 69115;Heidelberg Collaboratory for Image Processing & Image and Pattern Analysis Group, University of Heidelberg, Heidelberg, Germany 69115;Heidelberg Collaboratory for Image Processing & Image and Pattern Analysis Group, University of Heidelberg, Heidelberg, Germany 69115;Heidelberg Collaboratory for Image Processing & Image and Pattern Analysis Group, University of Heidelberg, Heidelberg, Germany 69115;Heidelberg Collaboratory for Image Processing & Image and Pattern Analysis Group, University of Heidelberg, Heidelberg, Germany 69115
Venue:
Computational Optimization and Applications
Year:
2013

Citing 14
Cited 0

The algebraic eigenvalue problem

The algebraic eigenvalue problem
Weakly differentiable functions

Weakly differentiable functions
Image selective smoothing and edge detection by nonlinear diffusion

SIAM Journal on Numerical Analysis
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
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures

Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection

International Journal of Computer Vision
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)
Non-local Regularization of Inverse Problems

ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Anisotropic Smoothing Using Double Orientations

SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal

SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Variational Methods in Imaging

Variational Methods in Imaging
A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science

SIAM Journal on Imaging Sciences
Variational image denoising with adaptive constraint sets

SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Forward-and-backward diffusion processes for adaptive image enhancement and denoising

IEEE Transactions on Image Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We introduce a class of adaptive non-smooth convex variational problems for image denoising in terms of a common data fitting term and a support functional as regularizer. Adaptivity is modeled by a set-valued mapping with closed, compact and convex values, that defines and steers the regularizer depending on the variational solution. This extension gives rise to a class of quasi-variational inequalities. We provide sufficient conditions for the existence of fixed points as solutions, and an algorithm based on solving a sequence of variational problems. Denoising experiments with spatial and spatio-temporal image data and an adaptive total variation regularizer illustrate our approach.