Optimized Projections for Compressed Sensing

• Published in: IEEE transactions on signal processing Vol. 55; no. 12; pp. 5695 - 5702
• Main Author: Elad, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-12-2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Basis pursuit (BP); Compressed; Compressed sensing; compressed sensing (CS); Compressing; Computer science; Detection; Detection, estimation, filtering, equalization, prediction; Dictionaries; Error analysis; Exact sciences and technology; Information, signal and communications theory; Iterative algorithms; Iterative methods; Linear systems; Matching pursuit algorithms; Miscellaneous; mutual coherence; Optimization; optimized projections; orthogonal matching pursuit (OMP); Projection; Pursuit algorithms; Representations; Signal and communications theory; Signal processing; Signal, noise; sparse and redundant representations; Telecommunications and information theory; optimized projections; orthogonal matching pursuit (OMP); Basis pursuit (BP); compressed sensing (CS); sparse and redundant representations; mutual coherence; Performance evaluation; Signal compression; Dictionaries; Error rate; Iterative method; Optimization; Matching pursuit; Signal processing; Sparse representation; Mutual coherence; Signal detection
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2007.900760

Compressed sensing (CS) offers a joint compression and sensing processes, based on the existence of a sparse representation of the treated signal and a set of projected measurements. Work on CS thus far typically assumes that the projections are drawn at random. In this paper, we consider the optimization of these projections. Since such a direct optimization is prohibitive, we target an average measure of the mutual coherence of the effective dictionary, and demonstrate that this leads to better CS reconstruction performance. Both the basis pursuit (BP) and the orthogonal matching pursuit (OMP) are shown to benefit from the newly designed projections, with a reduction of the error rate by a factor of 10 and beyond.