Recovery of frequency-sparse signals from compressive measurements

Marco F. Duarte, Richard G. Baraniuk

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

17 Scopus citations

Abstract

Compressive sensing (CS) is a new approach to simultaneous sensing and compression for sparse and compressible signals. While the discrete Fourier transform has been widely used for CS of frequency-sparse signals, it provides optimal sparse representations only for signals with components at integral frequencies. There exist redundant frames that provide compressible representations for frequency-sparse signals, but such frames are highly coherent and severely affect the performance of standard CS recovery. In this paper, we show that by modifying standard CS recovery algorithms to prevent coherent frame elements from being present in the signal estimate, it is possible to bypass the shortcomings introduced by the coherent frame. The resulting algorithm comes with theoretical guarantees and is shown to perform significantly better for frequency-sparse signal recovery than its standard counterparts. The algorithm can also be extended to similar settings that use coherent frames.

Original languageEnglish (US)
Title of host publication2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010
Pages599-606
Number of pages8
DOIs
StatePublished - Dec 1 2010
Event48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010 - Monticello, IL, United States
Duration: Sep 29 2010Oct 1 2010

Other

Other48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010
CountryUnited States
CityMonticello, IL
Period9/29/1010/1/10

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Control and Systems Engineering

Fingerprint

Dive into the research topics of 'Recovery of frequency-sparse signals from compressive measurements'. Together they form a unique fingerprint.

Cite this