27 September 2011 Sparse signal representations using the tunable Q-factor wavelet transform
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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.
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Ivan W. Selesnick, Ivan W. Selesnick, "Sparse signal representations using the tunable Q-factor wavelet transform", Proc. SPIE 8138, Wavelets and Sparsity XIV, 81381U (27 September 2011); doi: 10.1117/12.894280; https://doi.org/10.1117/12.894280

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