Low complexity projection-based adaptive algorithm for sparse system identification and signal reconstruction

Konstantinos Slavakis, Sergios Theodoridis, Isao Yamada

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

1 Scopus citations

Abstract

The present paper introduces a low complexity online convex analytic tool for time-varying sparse system identification and signal reconstruction tasks. The available information enters the design in two ways; (i) the sequentially arriving training data generate a sequence of simple closed convex sets, namely hyperslabs, and (ii) the information regarding the cardinality of the support of the unknown system/signal is used to create another sequence of closed convex sets, namely weighted ℓ1-balls. In such a way, searching for the unknown system/signal becomes the task of solving a convex feasibility problem with an infinite number of constraints. The basic tool to solve such a problem, with computational load that scales linearly to the number of unknowns, is the projection onto a closed convex set, and more importantly the subgradient projection mapping associated to a convex function. A convergence analysis of the proposed algorithm is given based on very recent advances of projection-based adaptive algorithms, and numerical results are presented to support the introduced theory.

Original languageEnglish (US)
Title of host publicationConference Record of the 44th Asilomar Conference on Signals, Systems and Computers, Asilomar 2010
Pages703-707
Number of pages5
DOIs
StatePublished - Dec 1 2010
Event44th Asilomar Conference on Signals, Systems and Computers, Asilomar 2010 - Pacific Grove, CA, United States
Duration: Nov 7 2010Nov 10 2010

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
ISSN (Print)1058-6393

Other

Other44th Asilomar Conference on Signals, Systems and Computers, Asilomar 2010
CountryUnited States
CityPacific Grove, CA
Period11/7/1011/10/10

Keywords

  • Adaptive filtering
  • convex sets
  • projection
  • sparsity
  • subgradient projection

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