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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 (2010) IEEE TRANSACTIONS ON SIGNAL PROCESSING. 58(7). p.3907-3912
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Autocorrelation functions, complex wavelets, NOISE ESTIMATION, TRANSFORM, DECOMPOSITIONS, DESIGN, IMAGES, DOMAIN, SIGNAL
journal title
IEEE TRANSACTIONS ON SIGNAL PROCESSING
IEEE Trans. Signal Process.
volume
58
issue
7
pages
3907 - 3912
Web of Science type
Article
Web of Science id
000278813600042
JCR category
ENGINEERING, ELECTRICAL & ELECTRONIC
JCR impact factor
2.631 (2010)
JCR rank
17/247 (2010)
JCR quartile
1 (2010)
ISSN
1053-587X
DOI
10.1109/TSP.2010.2047392
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1002600
handle
http://hdl.handle.net/1854/LU-1002600
date created
2010-07-05 18:15:35
date last changed
2016-12-19 15:46:25
@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},
}

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.