Weighted -$\ell_1$ minimization with multiple weighting sets

TitleWeighted -$\ell_1$ minimization with multiple weighting sets
Publication TypeConference
Year of Publication2011
AuthorsHassan Mansour, Ozgur Yilmaz
Conference NameProc. SPIE
Conference LocationUniversity of British Columbia, Vancouver
KeywordsCompressive Sensing, Optimization

In this paper, we study the support recovery conditions of weighted -$\ell_1$ minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. We identify a class of signals for which the recovered vector from -$\ell_1$ minimization provides an accurate support estimate. We then derive stability and robustness guarantees for the weighted -$\ell_1$ minimization problem with more than one support estimate. We show that applying a smaller weight to support estimate that enjoy higher accuracy improves the recovery conditions compared with the case of a single support estimate and the case with standard, i.e., non-weighted,-$\ell_1$ minimization. Our theoretical results are supported by numerical simulations on synthetic signals and real audio signals.

Citation KeyMansour11TRwmmw