Weighted -$\ell_1$ minimization with multiple weighting sets

 Title Weighted -$\ell_1$ minimization with multiple weighting sets Publication Type Conference Year of Publication 2011 Authors Hassan Mansour, Ozgur Yilmaz Conference Name Proc. SPIE Volume 8138 Number 813809 Page 813809-813809-13 Month 09 Conference Location University of British Columbia, Vancouver Keywords Compressive Sensing, Optimization Abstract 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. URL https://www.slim.eos.ubc.ca/Publications/Public/Conferences/SPIE/2011/Mansour11TRwmmw/Mansour11TRwmmw.pdf DOI 10.1117/12.894165 Citation Key Mansour11TRwmmw