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Compressed Sensing With Prior Information: Information-Theoretic Limits and Practical Decoders

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3 Author(s)
Jonathan Scarlett ; Department of Engineering, University of Cambridge, United Kingdom ; Jamie S. Evans ; Subhrakanti Dey

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=[x1,...,xN]T has a randomly generated sparsity pattern, where the i-th entry is non-zero with probability pi. 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.

Published in:

IEEE Transactions on Signal Processing  (Volume:61 ,  Issue: 2 )