Images, numerical analysis of singularities and shock filters
Images, numerical analysis of singularities and shock filters
The mathematics of nonlinear programming
The mathematics of nonlinear programming
Introduction to numerical linear algebra and optimisation
Introduction to numerical linear algebra and optimisation
Weakly differentiable functions
Weakly differentiable functions
Constrained Restoration and the Recovery of Discontinuities
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
A multiscale algorithm for image segmentation by variational method
SIAM Journal on Numerical Analysis
Variational methods in image segmentation
Variational methods in image segmentation
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
A Nonlinear Primal-Dual Method for 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
Journal of Mathematical Imaging and Vision
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
Variational denoising of partly textured images
Journal of Visual Communication and Image Representation
Robust solvers for inverse imaging problems using dense single-precision hardware
Journal of Mathematical Imaging and Vision
IEEE Transactions on Image Processing
Multiplicative Noise Removal with Spatially Varying Regularization Parameters
SIAM Journal on Imaging Sciences
Journal of Mathematical Imaging and Vision
Total Variation as a Local Filter
SIAM Journal on Imaging Sciences
Fourth-order variational model with local-constraints for denoising images with textures
International Journal of Computational Vision and Robotics
A statistical multiresolution strategy for image reconstruction
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Journal of Mathematical Imaging and Vision
Image Restoration via Tight Frame Regularization and Local Constraints
Journal of Scientific Computing
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The problem of recovering an image that has been blurred and corrupted with additive noise is ill-posed. Among the methods that have been proposed to solve this problem, one of the most successful ones is that of constrained Total Variation (TV) image restoration, proposed by L. Rudin, S. Osher, and E. Fatemi. In its original formulation, to ensure the satisfaction of constraints, TV restoration requires the estimation of a global parameter λ (a Lagrange multiplier). We observe that if λ is global, the constraints of the method are also satisfied globally, but not locally. The effect is that the restoration is better achieved in some regions of the image than in others. To avoid this, we propose a variant of the TV restoration model including, instead of a single constraint λ, a set of constraints λi, each one corresponding to a region Oi of the image. We discuss the existence and uniqueness of solutions of the proposed model and display some numerical experiments.