期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 61, 期 2, 页码 427-439出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2012.2225051
关键词
Basis pursuit; compressed sensing; compressive sampling; information-theoretic bounds; Lasso; orthogonal matching pursuit; prior information; sparsity pattern recovery; support recovery
This paper considers the problem of sparse signal recovery when the decoder has prior information on the sparsity pattern of the data. The data vector x = [x(1), ... , x(N)](T) has a randomly generated sparsity pattern, where the i-th entry is non-zero with probability p(i). Given knowledge of these probabilities, the decoder attempts to recover x based on M random noisy projections. Information-theoretic limits on the number of measurements needed to recover the support set of x perfectly are given, and it is shown that significantly fewer measurements can be used if the prior distribution is sufficiently non-uniform. Furthermore, extensions of Basis Pursuit, LASSO, and Orthogonal Matching Pursuit which exploit the prior information are presented. The improved performance of these methods over their standard counterparts is demonstrated using simulations.
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