Sparse decomposition of transformation-invariant signals with continuous basis pursuit

Chaitanya Ekanadham, Daniel Tranchina, Eero P. Simoncelli

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

Abstract

Consider the decomposition of a signal into features that undergo transformations drawn from a continuous family. Current methods discretely sample the transformations and apply sparse recovery methods to the resulting finite dictionary. These methods do not exploit the underlying continuous structure, thereby limiting the ability to produce sparse solutions. Instead, we employ interpolation functions which linearly approximate the manifold of scaled and transformed features. Coefficients are interpreted as interpolation weights, and we formulate a convex optimization problem for obtaining them, enforcing both reconstruction accuracy and sparsity. We compare our method, which we call continuous basis pursuit (CBP) with the standard basis pursuit approach on a sparse deconvolution task. CBP yields substantially sparser solutions without sacrificing accuracy, and does so with a smaller dictionary. We conclude that for signals generated by transformation-invariant processes, a representation that explicitly accommodates the transformation(s) can yield sparser and more interpretable decompositions.

Original languageEnglish (US)
Title of host publication2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
Pages4060-4063
Number of pages4
DOIs
StatePublished - 2011
Event36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Prague, Czech Republic
Duration: May 22 2011May 27 2011

Publication series

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

Other

Other36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011
CountryCzech Republic
CityPrague
Period5/22/115/27/11

Keywords

  • basis pursuit
  • feature decomposition
  • interpolation
  • invariance
  • sparsity

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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