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A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands

Bart Goossens (UGent) , Jan Aelterman (UGent) , Aleksandra Pizurica (UGent) and Wilfried Philips (UGent)
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Abstract
This paper deals with the problem of the exact computation of the autocorrelation function of a real or complex discrete wavelet subband of a signal, when the autocorrelation function (or Power Spectral Density, PSD) of the signal in the time domain (or spatial domain) is either known or estimated using a separate technique. The solution to this problem allows us to couple time domain noise estimation techniques to wavelet domain denoising algorithms, which is crucial for the development of blind wavelet-based denoising techniques. Specifically, we investigate the Dual-Tree complex wavelet transform (DT-CWT), which has a good directional selectivity in 2-D and 3-D, is approximately shift-invariant, and yields better denoising results than a discrete wavelet transform (DWT). The proposed scheme gives an analytical relationship between the PSD of the input signal/image and the PSD of each individual real/complex wavelet subband which is very useful for future developments. We also show that a more general technique, that relies on Monte-Carlo simulations, requires a large number of input samples for a reliable estimate, while the proposed technique does not suffer from this problem.
Keywords
Autocorrelation functions, complex wavelets, NOISE ESTIMATION, TRANSFORM, DECOMPOSITIONS, DESIGN, IMAGES, DOMAIN, SIGNAL

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Chicago
Goossens, Bart, Jan Aelterman, Aleksandra Pizurica, and Wilfried Philips. 2010. “A Recursive Scheme for Computing Autocorrelation Functions of Decimated Complex Wavelet Subbands.” Ieee Transactions on Signal Processing 58 (7): 3907–3912.
APA
Goossens, B., Aelterman, J., Pizurica, A., & Philips, W. (2010). A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 58(7), 3907–3912.
Vancouver
1.
Goossens B, Aelterman J, Pizurica A, Philips W. A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands. IEEE TRANSACTIONS ON SIGNAL PROCESSING. 2010;58(7):3907–12.
MLA
Goossens, Bart, Jan Aelterman, Aleksandra Pizurica, et al. “A Recursive Scheme for Computing Autocorrelation Functions of Decimated Complex Wavelet Subbands.” IEEE TRANSACTIONS ON SIGNAL PROCESSING 58.7 (2010): 3907–3912. Print.
@article{1002600,
  abstract     = {This paper deals with the problem of the exact computation of the autocorrelation function of a real or complex discrete wavelet subband of a signal, when the autocorrelation function (or Power Spectral Density, PSD) of the signal in the time domain (or spatial domain) is either known or estimated using a separate technique. The solution to this problem allows us to couple time domain noise estimation techniques to wavelet domain denoising algorithms, which is crucial for the development of blind wavelet-based denoising techniques. Specifically, we investigate the Dual-Tree complex wavelet transform (DT-CWT), which has a good directional selectivity in 2-D and 3-D, is approximately shift-invariant, and yields better denoising results than a discrete wavelet transform (DWT). The proposed scheme gives an analytical relationship between the PSD of the input signal/image and the PSD of each individual real/complex wavelet subband which is very useful for future developments. We also show that a more general technique, that relies on Monte-Carlo simulations, requires a large number of input samples for a reliable estimate, while the proposed technique does not suffer from this problem.},
  author       = {Goossens, Bart and Aelterman, Jan and Pizurica, Aleksandra and Philips, Wilfried},
  issn         = {1053-587X},
  journal      = {IEEE TRANSACTIONS ON SIGNAL PROCESSING},
  keyword      = {Autocorrelation functions,complex wavelets,NOISE ESTIMATION,TRANSFORM,DECOMPOSITIONS,DESIGN,IMAGES,DOMAIN,SIGNAL},
  language     = {eng},
  number       = {7},
  pages        = {3907--3912},
  title        = {A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands},
  url          = {http://dx.doi.org/10.1109/TSP.2010.2047392},
  volume       = {58},
  year         = {2010},
}

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