Random filters for compressive sampling and reconstruction

Joel A. Tropp, Michael B. Wakin, Marco F. Duarte, Dror Baron, Richard G. Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

236 Scopus citations

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.

Original languageEnglish (US)
Title of host publication2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings
Volume3
StatePublished - Dec 1 2006
Event2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006 - Toulouse, France
Duration: May 14 2006May 19 2006

Other

Other2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006
CountryFrance
CityToulouse
Period5/14/065/19/06

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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