Locally competitive algorithms for sparse approximation

Christopher Rozell, Don Johnson, Richard Baraniuk, Bruno Olshausen

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

23 Scopus citations

Abstract

Practical sparse approximation algorithms (particularly greedy algorithms) suffer two significant drawbacks: they are difficult to implement in hardware, and they are inefficient for time-varying stimuli (e.g., video) because they produce erratic temporal coefficient sequences. We present a class of locally competitive algorithms (LCAs) that correspond to a collection of sparse approximation principles minimizing a weighted combination of reconstruction MSE and a coefficient cost function. These systems use thresholding functions to induce local nonlinear competitions in a dynamical system. Simple analog hardware can implement the required nonlinearities and competitions. We show that our LCAs are stable under normal operating conditions and can produce sparsity levels comparable to existing methods. Additionally, these LCAs can produce coefficients for video sequences that are more regular (i.e., smoother and more predictable) than the coefficients produced by greedy algorithms.

Original languageEnglish (US)
Title of host publication2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Volume4
ISBN (Print)1424414377, 9781424414376
DOIs
StatePublished - Jan 1 2007
Event14th IEEE International Conference on Image Processing, ICIP 2007 - San Antonio, TX, United States
Duration: Sep 16 2007Sep 19 2007

Other

Other14th IEEE International Conference on Image Processing, ICIP 2007
CountryUnited States
CitySan Antonio, TX
Period9/16/079/19/07

Keywords

  • Approximation methods
  • Image coding
  • Nonlinear systems
  • Video coding
  • Visual system

ASJC Scopus subject areas

  • Engineering(all)

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