### 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(_{qr}N) 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 language | English |
---|---|

Pages (from-to) | 4557-4571 |

Number of pages | 15 |

Journal | IEEE Transactions on Signal Processing |

Volume | 54 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2006 Dec |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Signal Processing

### Cite this

**Pairwise optimal weight realization - Acceleration technique for set-theoretic adaptive parallel subgradient projection algorithm.** / Yukawa, Masahiro; Yamada, Isao.

Research output: Contribution to journal › Article

*IEEE Transactions on Signal Processing*, vol. 54, no. 12, pp. 4557-4571. https://doi.org/10.1109/TSP.2006.881225

}

TY - JOUR

T1 - Pairwise optimal weight realization - Acceleration technique for set-theoretic adaptive parallel subgradient projection algorithm

AU - Yukawa, Masahiro

AU - Yamada, Isao

PY - 2006/12

Y1 - 2006/12

N2 - 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.

AB - 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.

KW - Adaptive parallel subgradient projection

KW - Optimal weight design

KW - Set-theoretic adaptive filtering

UR - http://www.scopus.com/inward/record.url?scp=33947144069&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33947144069&partnerID=8YFLogxK

U2 - 10.1109/TSP.2006.881225

DO - 10.1109/TSP.2006.881225

M3 - Article

AN - SCOPUS:33947144069

VL - 54

SP - 4557

EP - 4571

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 12

ER -