Extension of the Global Matched Filter to structured groups of atoms: application to harmonic signals.
Résumé
When seeking a sparse representation of a signal on a redundant basis, one might want to convey available a priori information on the observations to the More or less efficient or elegant solutions to these problems have been proposed, modifying the penalty term in a sparse representation criterion is one of them. We show how to translate prior information by modifying the penalization term of the usual $\ell_2-\ell_1$ regularized criterion, we indicate how to tune the corresponding hyper-parameters by forming the dual of these modified criterion and we evaluate the associated performance on the sum of harmonics example.optimization criterion.
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