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A simple message-passing algorithm for compressed sensing

Author(s)
Chandar, Venkat B.; Shah, Devavrat; Wornell, Gregory W.
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Abstract
We consider the recovery of a nonnegative vector x from measurements y = Ax, where A ∈ {0, 1}[superscript m×n]. We establish that when A corresponds to the adjacency matrix of a bipartite graph with sufficient expansion, a simple message-passing algorithm produces an estimate x^ of x satisfying ∥x-x^∥[subscript 1] ≤ O(n/k) ∥x-x[superscript(k)]∥1, where x[superscript(k)] is the best k-sparse approximation of x. The algorithm performs O(n(log(n/k))[superscript 2] log (k)) computation in total, and the number of measurements required is m = O(k log(n/k)). In the special case when x is k-sparse, the algorithm recovers x exactly in time O(n log(n/k) log(k)). Ultimately, this work is a further step in the direction of more formally developing the broader role of message-passing algorithms in solving compressed sensing problems.
Date issued
2010-07
URI
http://hdl.handle.net/1721.1/72614
Department
Lincoln Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
IEEE International Symposium on Information Theory Proceedings 2010 (ISIT)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Chandar, Venkat, Devavrat Shah, and Gregory W. Wornell. “A Simple Message-passing Algorithm for Compressed Sensing.” IEEE International Symposium on Information Theory Proceedings 2010 (ISIT). 1968–1972. © Copyright 2010 IEEE
Version: Final published version
ISBN
978-1-4244-7891-0
978-1-4244-7890-3

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