Wavelet Denoising Based on the MAP Estimation Using the BKF Prior With Application to Images and EEG Signals

Boubchir, Larbi and Boashash, Boualem (2013) Wavelet Denoising Based on the MAP Estimation Using the BKF Prior With Application to Images and EEG Signals. Ieee Transactions On Signal Processing, 61 8: 1880-1894. doi:10.1109/TSP.2013.2245657


Author Boubchir, Larbi
Boashash, Boualem
Title Wavelet Denoising Based on the MAP Estimation Using the BKF Prior With Application to Images and EEG Signals
Journal name Ieee Transactions On Signal Processing   Check publisher's open access policy
ISSN 1053-587X
1941-0476
Publication date 2013-04
Year available 2013
Sub-type Article (original research)
DOI 10.1109/TSP.2013.2245657
Open Access Status
Volume 61
Issue 8
Start page 1880
End page 1894
Total pages 15
Place of publication Piscataway NJ USA
Publisher Institute of Electrical and Electronics Engineers
Collection year 2014
Language eng
Abstract This paper presents a novel nonparametric Bayesian estimator for signal and image denoising in the wavelet domain. This approach uses a prior model of the wavelet coefficients designed to capture the sparseness of the wavelet expansion. A new family of Bessel K Form (BKF) densities are designed to fit the observed histograms, so as to provide a probabilistic model for the marginal densities of the wavelet coefficients. This paper first shows how the BKF prior can characterize images belonging to Besov spaces. Then, a new hyper-parameters estimator based on EM algorithm is designed to estimate the parameters of the BKF density; and, it is compared with a cumulants-based estimator. Exploiting this prior model, another novel contribution is to design a Bayesian denoiser based on the Maximum A Posteriori (MAP) estimation under the 0–1 loss function, for which we formally establish the mathematical properties and derive a closed-form expression. Finally, a comparative study on a digitized database of natural images and biomedical signals shows the effectiveness of this new Bayesian denoiser compared to other classical and Bayesian denoising approaches. Results on biomedical data illustrate the method in the temporal as well as the time-frequency domain.
Keyword Bayesian denoising
Bayesian estimation
Besov space
Bessel K form prior
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: UQ Centre for Clinical Research Publications
Official 2014 Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 11 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 15 times in Scopus Article | Citations
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