Compressed sensing of time-varying signals

D. Angelosante, Georgios B Giannakis, E. Grossi

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

80 Scopus citations

Abstract

Compressed sensing (CS) lowers the number of measurements required for reconstruction and estimation of signals that are sparse when expanded over a proper basis. Traditional CS approaches deal with time-invariant sparse signals, meaning that, during the measurement process, the signal of interest does not exhibit variations. However, many signals encountered in practice are varying with time as the observation window increases (e.g., video imaging, where the signal is sparse and varies between different frames). The present paper develops CS algorithms for time-varying signals, based on the least-absolute shrinkage and selection operator (Lasso) that has been popular for sparse regression problems. The Lasso here is tailored for smoothing time-varying signals, which are modeled as vector valued discrete time series. Two algorithms are proposed: the Group-Fused Lasso, when the unknown signal support is time-invariant but signal samples are allowed to vary with time; and the Dynamic Lasso, for the general class of signals with time-varying amplitudes and support. Performance of these algorithms is compared with a sparsity-unaware Kalman smoother, a support-aware Kalman smoother, and the standard Lasso which does not account for time variations. The numerical results amply demonstrate the practical merits of the novel CS algorithms.

Original languageEnglish (US)
Title of host publicationDSP 2009:16th International Conference on Digital Signal Processing, Proceedings
DOIs
StatePublished - Nov 20 2009
EventDSP 2009:16th International Conference on Digital Signal Processing - Santorini, Greece
Duration: Jul 5 2009Jul 7 2009

Publication series

NameDSP 2009: 16th International Conference on Digital Signal Processing, Proceedings

Other

OtherDSP 2009:16th International Conference on Digital Signal Processing
CountryGreece
CitySantorini
Period7/5/097/7/09

Keywords

  • Compressed sensing
  • Fused lasso
  • Group lasso
  • Lasso
  • Smoothing
  • Tracking

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