Recovering Compressively Sampled Signals Using Partial Support Information

2011/09/15 by Michael P. Friedlander, Hassan Mansour, Rayan Saab +2 · 269 citations
Computer Science · Engineering · #Algorithm #Artificial intelligence #Compressed sensing #Computer science #Distributed Sensor Networks and Detection Algorithms #Microwave Imaging and Scattering Analysis #Minification #Sparse and Compressive Sensing Techniques #World Wide Web

paper · doi:10.1109/tit.2011.2167214

published in IEEE Transactions on Information Theory 58(2), 1122-1134 (Institute of Electrical and Electronics Engineers)

openalex publication_date 2011/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study recovery conditions of weightedl1minimization 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 weightedl1minimization is stable and robust under weaker sufficient conditions than the analogous conditions for standardl1minimization. Moreover, weightedl1minimization 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.

Citations

• Stable signal recovery from incomplete and inaccurate measurements
• Compressed sensing

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