Recovering compressively sampled signals using partial support information

TitleRecovering compressively sampled signals using partial support information
Publication TypeJournal Article
Year of Publication2012
AuthorsMichael P. Friedlander, Hassan Mansour, Rayan Saab, Ozgur Yilmaz
JournalIEEE Transactions on Information Theory
KeywordsCompressive Sensing

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.

Citation Keymansour2012IEEETITrcs