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AuthorBoubchir, Larbi
AuthorBoashash, Boualem
Available date2013-09-17T16:15:58Z
Publication Date2013-02-07
Publication NameIEEE Transactions on Signal Processing
CitationL. Boubchir and B. Boashash, "Wavelet denoising based on the MAP estimation using the BKF prior with application to images and EEG signals", IEEE Transactions on Signal Processing, vol. 61, no. 6, pp 1880-1894, April 2013.
DescriptionThis paper presents a wavelet-based Bayesian denoiser based on the MAP estimation using the BKF prior that is well adapted to characterize images that are described in the Besov spaces. (Additional details can be found in the comprehensive book on Time-Frequency Signal Analysis and Processing (see In addition, the most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia, and then continuously updated).
AbstractThis 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.
SubjectBayesian denoising
Bayesian estimation
Besov space
Bessel K form prior
EEG signal
EM algorithm
hyper-parameters estimation
maximum A posterior
statistical modeling
time-frequency image
TitleWavelet Denoising Based on the MAP Estimation Using the BKF Prior With Application to Images and EEG Signals

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