Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
Neural Computation
Extensions of compressed sensing
Signal Processing - Sparse approximations in signal and image processing
Algorithms for simultaneous sparse approximation: part I: Greedy pursuit
Signal Processing - Sparse approximations in signal and image processing
Algorithms for simultaneous sparse approximation: part II: Convex relaxation
Signal Processing - Sparse approximations in signal and image processing
Inpainting and Zooming Using Sparse Representations
The Computer Journal
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Dictionary learning for L1-exact sparse coding
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Vector-valued image regularization with PDE's: a common framework for different applications
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Recovery of sparse representations by polytope faces pursuit
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Sparse solutions to linear inverse problems with multiple measurement vectors
IEEE Transactions on Signal Processing
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
A generalized uncertainty principle and sparse representation in pairs of bases
IEEE Transactions on Information Theory
On sparse representation in pairs of bases
IEEE Transactions on Information Theory
Sparse representations in unions of bases
IEEE Transactions on Information Theory
On sparse representations in arbitrary redundant bases
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Why Simple Shrinkage Is Still Relevant for Redundant Representations?
IEEE Transactions on Information Theory
Disocclusion: a variational approach using level lines
IEEE Transactions on Image Processing
The curvelet transform for image denoising
IEEE Transactions on Image Processing
Sparse geometric image representations with bandelets
IEEE Transactions on Image Processing
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
The contourlet transform: an efficient directional multiresolution image representation
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Sparsity and Morphological Diversity in Blind Source Separation
IEEE Transactions on Image Processing
Morphological Component Analysis: An Adaptive Thresholding Strategy
IEEE Transactions on Image Processing
IEEE Transactions on Information Theory
An overview of inverse problem regularization using sparsity
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
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Over the last decade, overcomplete dictionaries and the very sparse signal representations they make possible, have raised an intense interest from signal processing theory. In a wide range of signal processing problems, sparsity has been a crucial property leading to high performance. As multichannel data are of growing interest, it seems essential to devise sparsity-based tools accounting for such specific multichannel data. Sparsity has proved its efficiency in a wide range of inverse problems. Hereafter, we address some multichannel inverse problems issues such as multichannel morphological component separation and inpainting from the perspective of sparse representation. In this paper, we introduce a new sparsity-based multichannel analysis tool coined multichannel Morphological Component Analysis (mMCA). This new framework focuses on multichannel morphological diversity to better represent multichannel data. This paper presents conditions under which the mMCA converges and recovers the sparse multichannel representation. Several experiments are presented to demonstrate the applicability of our approach on a set of multichannel inverse problems such as morphological component decomposition and inpainting.