Mathematical Programming: Series A and B
Convergence of a block coordinate descent method for nondifferentiable minimization
Journal of Optimization Theory and Applications
Dictionary learning algorithms for sparse representation
Neural Computation
Algorithms for simultaneous sparse approximation: part II: Convex relaxation
Signal Processing - Sparse approximations in signal and image processing
Method of optimal directions for frame design
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 05
Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints
SIAM Journal on Numerical Analysis
Dictionary learning for sparse approximations with the majorization method
IEEE Transactions on Signal Processing
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
Nested Iterative Algorithms for Convex Constrained Image Recovery Problems
SIAM Journal on Imaging Sciences
Recursive least squares dictionary learning algorithm
IEEE Transactions on Signal Processing
Foundations and Trends® in Machine Learning
-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
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Parallel Proximal Algorithm for Image Restoration Using Hybrid Regularization
IEEE Transactions on Image Processing
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This paper revisits the problem of dictionary learning on several points although we still consider an alternating optimization scheme. Our first contribution consists in providing a simple proof of convergence for this numerical scheme for a large class of constraints and regularizers on the dictionary atoms. We also investigate the use of a well-known optimization method named alternating direction method of multipliers for solving each of the alternate step of the dictionary learning problem. We show that such an algorithm yields to several benefits. Indeed, it can be more efficient than other competing algorithms such as Iterative Shrinkage Thresholding approach and besides, it allows one to easily deal with mixed constraints or regularizers over the dictionary atoms or approximation coefficients. For instance, we have induced joint sparsity, positivity and smoothness on the dictionary atoms by means of some total variation and sparsity-inducing regularizers. Our experimental results prove that using these mixed constraints helps in achieving better learned dictionary elements especially when learning from noisy signals.