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Random Filters for Compressive Sampling and Reconstruction

Tropp, Joel A. and Wakin, Michael . and Duarte, Marco F. and Baron, Dror and Baraniuk, Richard G. (2006) Random Filters for Compressive Sampling and Reconstruction. In: International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2006), Toulouse, France, 14-19 May 2006. Vol.III. IEEE , Piscataway, NJ, III-872. ISBN 1-4244-0469-X. http://resolver.caltech.edu/CaltechAUTHORS:TROicassp06

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Abstract

We propose and study a new technique for efficiently acquiring and reconstructing signals based on convolution with a fixed FIR filter having random taps. The method is designed for sparse and compressible signals, i.e., ones that are well approximated by a short linear combination of vectors from an orthonormal basis. Signal reconstruction involves a non-linear Orthogonal Matching Pursuit algorithm that we implement efficiently by exploiting the nonadaptive, time-invariant structure of the measurement process. While simpler and more efficient than other random acquisition techniques like Compressed Sensing, random filtering is sufficiently generic to summarize many types of compressible signals and generalizes to streaming and continuous-time signals. Extensive numerical experiments demonstrate its efficacy for acquiring and reconstructing signals sparse in the time, frequency, and wavelet domains, as well as piecewise smooth signals and Poisson processes.


Item Type:Book Section
ORCID:
AuthorORCID
Tropp, Joel A.0000-0003-1024-1791
Baraniuk, Richard G.0000-0002-0721-8999
Additional Information:© 2006 IEEE. Reprinted with permission. [Posted online: 2006-07-24] JAT was supported by NSF DMS grant 0503299. MBW, MFD, DB, and RGB were supported by NSF-CCF, NSF-NeTS, ONR, and AFOSR.
Funders:
Funding AgencyGrant Number
NSFUNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Record Number:CaltechAUTHORS:TROicassp06
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:TROicassp06
Alternative URL:http://dx.doi.org/10.1109/ICASSP.2006.1660793
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9065
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:25 Oct 2007
Last Modified:07 Apr 2017 19:28

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