# Recovering compressively sampled signals using partial support information

 Title Recovering compressively sampled signals using partial support information Publication Type Journal Article Year of Publication 2012 Authors Michael P. Friedlander, Hassan Mansour, Rayan Saab, Ozgur Yilmaz Journal IEEE Transactions on Information Theory Volume 58 Number 2 Page 1122-1134 Month 2 Publisher Department of Computer Science Keywords Compressive Sensing Abstract We study recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that if at least 50% of the (partial) support information is accurate, then weighted $\ell_1$ minimization is stable and robust under weaker sufficient conditions than the analogous conditions for standard $\ell_1$ minimization. Moreover, weighted $\ell_1$ minimization provides better upper bounds on the reconstruction error in terms of the measurement noise and the compressibility of the signal to be recovered. We illustrate our results with extensive numerical experiments on synthetic data and real audio and video signals. URL https://www.slim.eos.ubc.ca/Publications/Public/Journals/IEEETransInformationTheory/2012/mansour2012IEEETITrcs/mansour2012IEEETITrcs.pdf DOI 10.1109/TIT.2011.2167214 Citation Key mansour2012IEEETITrcs