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Proceedings Paper

Sparse signal representations using the tunable Q-factor wavelet transform
Author(s): Ivan W. Selesnick
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Paper Abstract

The tunable Q-factor wavelet transform (TQWT) is a fully-discrete wavelet transform for which the Q-factor, Q, of the underlying wavelet and the asymptotic redundancy (over-sampling rate), r, of the transform are easily and independently specified. In particular, the specified parameters Q and r can be real-valued. Therefore, by tuning Q, the oscillatory behavior of the wavelet can be chosen to match the oscillatory behavior of the signal of interest, so as to enhance the sparsity of a sparse signal representation. The TQWT is well suited to fast algorithms for sparsity-based inverse problems because it is a Parseval frame, easily invertible, and can be efficiently implemented using radix-2 FFTs. The TQWT can also be used as an easily-invertible discrete approximation of the continuous wavelet transform.

Paper Details

Date Published: 27 September 2011
PDF: 15 pages
Proc. SPIE 8138, Wavelets and Sparsity XIV, 81381U (27 September 2011); doi: 10.1117/12.894280
Show Author Affiliations
Ivan W. Selesnick, Polytechnic Institute of New York Univ. (United States)

Published in SPIE Proceedings Vol. 8138:
Wavelets and Sparsity XIV
Manos Papadakis; Dimitri Van De Ville; Vivek K. Goyal, Editor(s)

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