Accelerating ISTA with an active set strategy
Résumé
Starting from a practical implementation of Roth and Fisher's algorithm to solve a Lasso-type problem, we propose and study the Active Set Iterative Shrinkage/Thresholding Algorithm (AS-ISTA). The convergence is proven by observing that the algorithm can be seen as a particular case of a coordinate gradient descent algorithm with a Gauss-Southwell-r rule. We provide experimental evidence that the proposed method can outperform FISTA and significantly speed-up the resolution of very undetermined inverse problems when using sparse convex priors. The proposed algorithm makes brain mapping with magneto- and electroencephalography (M/EEG) significantly faster when promoting spatially sparse and temporally smooth solutions using a ''group-Lasso'' $\ell_{21}$ mixed-norm.
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