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Polynomial dictionary learning algorithms in sparse representations

Guan, Jian, Wang, Xuan, Feng, Pengming, Dong, Jing, Chambers, Jonathon, Jiang, Zoe L. and Wang, Wenwu (2017) Polynomial dictionary learning algorithms in sparse representations Signal Processing, 142. pp. 492-503.

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Dictionary learning has been extensively studied in sparse representations. However, existing dictionary learning algorithms are developed mainly for standard matrices (i.e. matrices with scalar elements), and little attention has been paid to polynomial matrices, despite their wide use for describing convolutive signals or for modeling acoustic channels in room and underwater acoustics. In this paper, we propose a polynomial dictionary learning technique to deal with signals with time delays. We present two types of polynomial dictionary learning methods based on the fact that a polynomial matrix can be represented either as a polynomial of matrices (i.e. the coefficient in the polynomial corresponding to each time lag is a scalar matrix) or equally as a matrix of polynomial elements (i.e. each element of the matrix is a polynomial). The first method allows one to extend any state-of-the-art dictionary learning method to the polynomial case; and the second method allows one to directly process the polynomial matrix without having to access its coefficient matrices. A sparse coding method is also presented for reconstructing convolutive signals based on a polynomial dictionary. Simulations are provided to demonstrate the performance of the proposed algorithms, e.g. for polynomial signal reconstruction from noisy measurements.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
Guan, Jian
Wang, Xuan
Feng, Pengming
Dong, Jing
Chambers, Jonathon
Jiang, Zoe L.
Date : 14 August 2017
Funders : Engineering and Physical Sciences Research Council (EPSRC )
DOI : 10.1016/j.sigpro.2017.08.011
Copyright Disclaimer : © 2017 Published by Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Uncontrolled Keywords : Dictionary learning; Polynomial matrix; Impulse responses; Sparse representation
Depositing User : Clive Harris
Date Deposited : 04 Sep 2017 15:05
Last Modified : 15 Aug 2019 02:08

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