Ten lectures on wavelets
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
Journal of Computational Physics
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints
SIAM Journal on Numerical Analysis
Adaptive iterative thresholding algorithms for magnetoencephalography (MEG)
Journal of Computational and Applied Mathematics
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
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
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration
Journal of Scientific Computing
A Modified TV-Stokes Model for Image Processing
SIAM Journal on Scientific Computing
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We propose an iterative algorithm for the minimization of a 驴 1-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices present in the problem (in the linear constraint, in the data misfit part and in the penalty term of the functional). None of the three matrices must be invertible. Convergence is proven in a finite-dimensional setting. We apply the algorithm to a synthetic problem in magneto-encephalography where it is used for the reconstruction of divergence-free current densities subject to a sparsity promoting penalty on the wavelet coefficients of the current densities. We discuss the effects of imposing zero divergence and of imposing joint sparsity (of the vector components of the current density) on the current density reconstruction.