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
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Edge Direction Preserving Image Zooming: A Mathematical and Numerical Analysis
SIAM Journal on Numerical Analysis
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Image Decomposition into a Bounded Variation Component and an Oscillating Component
Journal of Mathematical Imaging and Vision
Exploratory basis pursuit classification
Pattern Recognition Letters - Special issue: Artificial neural networks in pattern recognition
Image Compression Through a Projection onto a Polyhedral Set
Journal of Mathematical Imaging and Vision
IEEE Transactions on Information Theory
Minimizing the total variation under a general convex constraint for image restoration
IEEE Transactions on Image Processing
Image restoration subject to a total variation constraint
IEEE Transactions on Image Processing
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
A Predual Proximal Point Algorithm Solving a Non Negative Basis Pursuit Denoising Model
International Journal of Computer Vision
Total Variation as a Local Filter
SIAM Journal on Imaging Sciences
Hi-index | 0.08 |
This paper focuses on optimization problems containing an l^1 kind of regularity criterion and a smooth data fidelity term. A general theorem is applied in this context; it gives an estimate of the distribution law of the ''rank'' of the solution to optimization problems, when the initial datum follows a uniform (in a convex compact set) distribution law. It says that, asymptotically, solutions with a large rank are more and more likely. The main goal of this paper is to understand the meaning of this notion of rank for some energies which are commonly used in image processing. We study in detail the energy whose level sets are defined as the convex hull of a finite subset of R^N (c.f. Basis Pursuit) and the total variation. For these energies, the notion of rank relates, respectively, to sparse representation and staircasing. In all cases but the 2D total variation, we are able to adapt the general theorem mentioned above to the energies under consideration.