Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
Matrix analysis
Visual reconstruction
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
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
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
Recovery of blocky images from noisy and blurred data
SIAM Journal on Applied Mathematics
International Journal of Computer Vision
Practical Aspects of the Moreau--Yosida Regularization: Theoretical Preliminaries
SIAM Journal on Optimization
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
A unified approach to statistical tomography using coordinate descent optimization
IEEE Transactions on Image Processing
Total variation blind deconvolution
IEEE Transactions on Image Processing
An axiomatic approach to image interpolation
IEEE Transactions on Image Processing
Markovian reconstruction using a GNC approach
IEEE Transactions on Image Processing
A comparison of three total variation based texture extraction models
Journal of Visual Communication and Image Representation
Staircasing in semidiscrete stabilised inverse linear diffusion algorithms
Journal of Computational and Applied Mathematics
Image restoration combining a total variational filter and a fourth-order filter
Journal of Visual Communication and Image Representation
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
An Improved LOT Model for Image Restoration
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Multiplicative Noise Cleaning via a Variational Method Involving Curvelet Coefficients
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
Journal of Mathematical Imaging and Vision
Counter-examples for Bayesian MAP restoration
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Bounds on the minimizers of (nonconvex) regularized least-squares
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Total Variation as a Local Filter
SIAM Journal on Imaging Sciences
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
A variational approach for exact histogram specification
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Exact Histogram Specification for Digital Images Using a Variational Approach
Journal of Mathematical Imaging and Vision
A Framework for Moving Least Squares Method with Total Variation Minimizing Regularization
Journal of Mathematical Imaging and Vision
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We focus on the question of how the shape of a cost-function determines the features manifested by its local (and hence global) minimizers. Our goal is to check the possibility that the local minimizers of an unconstrained cost-function satisfy different subsets of affine constraints dependent on the data, hence the word “weak”. A typical example is the estimation of images and signals which are constant on some regions. We provide general conditions on cost-functions which ensure that their minimizers can satisfy weak constraints when noisy data range over an open subset. These cost-functions are non-smooth at all points satisfying the weak constraints. In contrast, the local minimizers of smooth cost-functions can almost never satisfy weak constraints. These results, obtained in a general setting, are applied to analyze the minimizers of cost-functions, composed of a data-fidelity term and a regularization term. We thus consider the effect produced by non-smooth regularization, in comparison with smooth regularization. In particular, these results explain the stair-casing effect, well known in total-variation methods. Theoretical results are illustrated using analytical examples and numerical experiments.