Near-optimal Binary Compressed Sensing Matrix
Résumé
Compressed sensing is a promising technique in signal processing that attempts to recover sparse signal through as few linear and nonadaptive measurements as possible. In this sense, the recovery performance is largely determined by the structure of measurement matrix. Recently, (0,1) binary random matrix is found attractive for its lower computation load as well as for its comparable performance with Gaussian Matrix. However, the optimal distribution of binary random matrix for compressed sensing remain unknown in theory. This paper, for the first time, deterministically defines one class of near- optimal binary random matrix by comparing the restricted isometry property (RIP) of regular binary random matrix characterized with the correlation between columns. And in theory, the proposed matrix is expected to achieve nearly the best RIP with as few nonzero entries as possible. Simulation results also confirm the availability of the proposed near-optimal matrix, with better performance over both traditional binary random matrix and Gaussian matrix.
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