Wavelet-domain compressive signal reconstruction using a Hidden Markov Tree Model

Marco F. Duarte, Michael B. Wakin, Richard G. Baraniuk

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

93 Scopus citations

Abstract

Compressive sensing aims to recover a sparse or compressible signal from a small set of projections onto random vectors; conventional solutions involve linear programming or greedy algorithms that can be computationally expensive. Moreover, these recovery techniques are generic and assume no particular structure in the signal aside from sparsity. In this paper, we propose a new algorithm that enables fast recovery of piecewise smooth signals, a large and useful class of signals whose sparse wavelet expansions feature a distinct "connected tree" structure. Our algorithm fuses recent results on iterative reweighted l1-norm minimization with the wavelet Hidden Markov Tree model. The resulting optimization-based solver outperforms the standard compressive recovery algorithms as well as previously proposed wavelet-based recovery algorithms. As a bonus, the algorithm reduces the number of measurements necessary to achieve low-distortion reconstruction.

Original languageEnglish (US)
Title of host publication2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
Pages5137-5140
Number of pages4
DOIs
StatePublished - 2008
Event2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP - Las Vegas, NV, United States
Duration: Mar 31 2008Apr 4 2008

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
CountryUnited States
CityLas Vegas, NV
Period3/31/084/4/08

Keywords

  • Compressive sensing
  • Data compression
  • Hidden Markov Models
  • Signal reconstruction
  • Wavelet transforms

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing
  • Acoustics and Ultrasonics

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