A simple message-passing algorithm for compressed sensing
Name
Shah_A simple message-passing.pdf
Size
199.07 KB
Format
Adobe PDF
Checksum (MD5)
97a10f7d2d0a14f4fec47a7ed0626975
Author(s)
Chandar, Venkat B.
Shah, Devavrat
Wornell, Gregory W.
Date Issued
July 2010
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
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.
MIT Department
Lincoln Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/ISIT.2010.5513358
