Optimal overcomplete kernel design for sparse representations via discrete fractional Fourier transforms

Yang, Zhijing, Qing, Chunmei, Ling, Bingo Wing-Kuen, Woo, Wai Lok and Sanei, Saeid (2012) Optimal overcomplete kernel design for sparse representations via discrete fractional Fourier transforms. In: 2012 8th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP). IEEE. ISBN 978-1-4577-1472-6

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Abstract

This paper proposes to use a set of discrete fractional Fourier transform (DFrFT) matrices with different rotational angles to construct an overcomplete kernel for sparse representations of signals. The design of the rotational angles is formulated as an optimization problem. To solve the problem, it is shown that this design problem is equivalent to an optimal sampling problem. Furthermore, the optimal sampling frequencies are the roots of a set of harmonic functions. As the frequency responses of the filters are required to be computed only at frequencies in a discrete set, the globally optimal rotational angles can be found very efficiently and effectively.

Item Type:	Book Section
Subjects:	G400 Computer Science
Department:	Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User:	Becky Skoyles
Date Deposited:	10 May 2019 14:11
Last Modified:	10 Oct 2019 19:02
URI:	http://nrl.northumbria.ac.uk/id/eprint/39263

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