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Compressed Sensing

Optimized Projection Directions for Compressed Sensing
June 20th, 2007
The IV workshop on SIP & IT, Holon Institute of Technology, Holon.

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 talk we describe ways to optimize these projections. Two methods are considered: (i) A direct optimization with respect to the CS performance, targeting CS applied with the Orthogonal Matching Pursuit (OMP) or Basis Pursuit (BP), and (ii) A simpler method that targets an average measure of the mutual-coherence of the effective dictionary. As the first approach leads to a complex bi-level optimization task that is hard to handle, we demonstrate the second one and show that it leads to better CS reconstruction performance.

This talk was also given in MVP seminar in Tel-Aviv university on June 21st, and also in ICIAM, Zurich, on July 17th, 2007.