Pairwise optimal weight realization - Acceleration technique for set-theoretic adaptive parallel subgradient projection algorithm

Masahiro Yukawa, Isao Yamada

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

The adaptive parallel subgradient projection (PSP) algorithm was proposed in 2002 as a set-theoretic adaptive filtering algorithm providing fast and stable convergence, robustness against noise, and low computational complexity by using weighted parallel projections onto multiple time-varying closed half-spaces. In this paper, we present a novel weighting technique named pairwise optimal weight realization (POWER) for further acceleration of the adaptive PSP algorithm. A simple closed-form formula is derived to compute the projection onto the intersection of two closed half-spaces defined by a triplet of vectors. Using the formula inductively, the proposed weighting technique realizes a good direction of update. The resulting weights turn out to be pairwise optimal in a certain sense. The proposed algorithm has the inherently parallel structure composed of q primitive functions, hence its total computational complexity O(qrN) is reduced to O(rN) with q concurrent processors (r: a constant positive integer). Numerical examples demonstrate that the proposed technique for r =1 yields significantly faster convergence than not only adaptive PSP with uniform weights, affine projection algorithm, and fast Newton transversal filters but also the regularized recursive least squares algorithm.

Original languageEnglish
Pages (from-to)4557-4571
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume54
Issue number12
DOIs
Publication statusPublished - 2006 Dec
Externally publishedYes

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Computational complexity
Transversal filters
Adaptive filtering

Keywords

  • Adaptive parallel subgradient projection
  • Optimal weight design
  • Set-theoretic adaptive filtering

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

Cite this

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abstract = "The adaptive parallel subgradient projection (PSP) algorithm was proposed in 2002 as a set-theoretic adaptive filtering algorithm providing fast and stable convergence, robustness against noise, and low computational complexity by using weighted parallel projections onto multiple time-varying closed half-spaces. In this paper, we present a novel weighting technique named pairwise optimal weight realization (POWER) for further acceleration of the adaptive PSP algorithm. A simple closed-form formula is derived to compute the projection onto the intersection of two closed half-spaces defined by a triplet of vectors. Using the formula inductively, the proposed weighting technique realizes a good direction of update. The resulting weights turn out to be pairwise optimal in a certain sense. The proposed algorithm has the inherently parallel structure composed of q primitive functions, hence its total computational complexity O(qrN) is reduced to O(rN) with q concurrent processors (r: a constant positive integer). Numerical examples demonstrate that the proposed technique for r =1 yields significantly faster convergence than not only adaptive PSP with uniform weights, affine projection algorithm, and fast Newton transversal filters but also the regularized recursive least squares algorithm.",
keywords = "Adaptive parallel subgradient projection, Optimal weight design, Set-theoretic adaptive filtering",
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