Introduction to numerical linear algebra and optimisation
Introduction to numerical linear algebra and optimisation
On the convergence of the proximal point algorithm for convex minimization
SIAM Journal on Control and Optimization
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Practical Aspects of the Moreau--Yosida Regularization: Theoretical Preliminaries
SIAM Journal on Optimization
Exploratory basis pursuit classification
Pattern Recognition Letters - Special issue: Artificial neural networks in pattern recognition
Proximal Thresholding Algorithm for Minimization over Orthonormal Bases
SIAM Journal on Optimization
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Why Simple Shrinkage Is Still Relevant for Redundant Representations?
IEEE Transactions on Information Theory
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
On the total variation dictionary model
IEEE Transactions on Image Processing
A novel predual dictionary learning algorithm
Journal of Visual Communication and Image Representation
An augmented Lagrangian approach to general dictionary learning for image denoising
Journal of Visual Communication and Image Representation
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This paper develops an implementation of a Predual Proximal Point Algorithm (PPPA) solving a Non Negative Basis Pursuit Denoising model. The model imposes a constraint on the l 2 norm of the residual, instead of penalizing it. The PPPA solves the predual of the problem with a Proximal Point Algorithm (PPA). Moreover, the minimization that needs to be performed at each iteration of PPA is solved with a dual method. We can prove that these dual variables converge to a solution of the initial problem.Our analysis proves that we turn a constrained non differentiable convex problem into a short sequence of nice concave maximization problems. By nice, we mean that the functions which are maximized are differentiable and their gradient is Lipschitz.The algorithm is easy to implement, easier to tune and more general than the algorithms found in the literature. In particular, it can be applied to the Basis Pursuit Denoising (BPDN) and the Non Negative Basis Pursuit Denoising (NNBPDN) and it does not make any assumption on the dictionary. We prove its convergence to the set of solutions of the model and provide some convergence rates.Experiments on image approximation show that the performances of the PPPA are at the current state of the art for the BPDN.