Larbi Boubchir

Analytical form for a Bayesian wavelet estimator of images using the Bessel K form densities

A novel Bayesian nonparametric estimator in the wavelet domain is presented. In this approach, a prior model is imposed on the wavelet coefficients designed to capture the sparseness of the wavelet expansion. Seeking probability models for the marginal densities of the wavelet coefficients, the new family of Bessel K forms (BKF) densities are shown to fit very well to the observed histograms. Exploiting this prior, we designed a Bayesian nonlinear denoiser and we derived a closed form for its expression. We then compared it to other priors that have been introduced in the literature, such as the generalized Gaussian density (GGD) or the /spl alpha/-stable models, where no analytical form is available for the corresponding Bayesian denoisers. Specifically, the BKF model turns out to be a good compromise between these two extreme cases (hyperbolic tails for the /spl alpha/-stable and exponential tails for the GGD). Moreover, we demonstrate a high degree of match between observed and estimated prior densities using the BKF model. Finally, a comparative study is carried out to show the effectiveness of our denoiser which clearly outperforms the classical shrinkage or thresholding wavelet-based techniques.

A closed-form nonparametric Bayesian estimator in the wavelet domain of images using an approximate α-stable prior

In this paper, a nonparametric Bayesian estimator in the wavelet domains is presented. In this approach, we propose a prior statistical model based on the @a-stable densities adapted to capture the sparseness of the wavelet detail coefficients. An attempt to apply this model in the context of wavelet denoising have been already proposed in (Achim, A., Bezerianos, A., Tsakalides, P., 2001. Novel Bayesian multiscale method for speckle removal in medical ultrasound images. IEEE Trans. Med. Imag. 20, 772-783). However, despite its efficacy in modeling the heavy tail behavior of the empirical wavelet coefficients histograms, their denoiser proves very poor in practice especially at low SNRs. It suffers from many drawbacks such as numerical instability because of the lack of a closed-form expression of the Bayesian shrinkage rule, and the weakness of the estimator of the hyperparameters associated with the @a-stable prior. Here, we propose to overcome these limitations using the scale mixture of Gaussians theorem as an analytical approximation for @a-stable densities, which is not known in general, in order to obtain a closed-form expression of our Bayesian denoiser.

A methodology for time-frequency image processing applied to the classification of non-stationary multichannel signals using instantaneous frequency descriptors with application to newborn EEG signals

This article presents a general methodology for processing non-stationary signals for the purpose of classification and localization. The methodology combines methods adapted from three complementary areas: time-frequency signal analysis, multichannel signal analysis and image processing. The latter three combine in a new methodology referred to as multichannel time-frequency image processing which is applied to the problem of classifying electroencephalogram (EEG) abnormalities in both adults and newborns. A combination of signal related features and image related features are used by merging key instantaneous frequency descriptors which characterize the signal non-stationarities. The results obtained show that, firstly, the features based on time-frequency image processing techniques such as image segmentation, improve the performance of EEG abnormalities detection in the classification systems based on multi-SVM and neural network classifiers. Secondly, these discriminating features are able to better detect the correlation between newborn EEG signals in a multichannel-based newborn EEG seizure detection for the purpose of localizing EEG abnormalities on the scalp.

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

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.

Time-frequency signal and image processing of non-stationary signals with application to the classification of newborn EEG abnormalities

This paper presents an introduction to time-frequency (T-F) methods in signal processing, and a novel approach for EEG abnormalities detection and classification based on a combination of signal related features and image related features. These features which characterize the non-stationary nature and the multi-component characteristic of EEG signals, are extracted from the T-F representation of the signals. The signal related features are derived from the T-F representation of EEG signals and include the instantaneous frequency, singular value decomposition, and energy based features. The image related features are extracted from the T-F representation considered as an image, using T-F image processing techniques. These combined signal and image features allow to extract more information from a signal. The results obtained on newborn and adult EEG data, show that the image related features improve the performance of the EEG seizure detection in classification systems based on multi-SVM classifier.

Improving the classification of newborn EEG time-frequency representations using a combined time-frequency signal and image approach

This paper presents new time-frequency (T-F) features to improve the classification of non-stationary signals such as EEG signals. Previous methods were based only on signal features that were derived from the instantaneous frequency and energies of EEG signals in different spectral sub-bands. This paper includes new features that are based on T-F image descriptors which are extracted from the T-F representation considered as an image, using T-F image processing techniques. The results obtained on newborn EEG data, show that the use of image related-features with signal based-features improve the performance of the newborn EEG seizure detection and classification when using multi-SVM classifiers. These results allow the possibility of improving health outcomes for sick babies by early intervention on the basis of the results of the classification of newborn EEG abnormalities.

Morphological Diversity and Sparse Image Denoising

Overcomplete representations are attracting interest in image processing theory, particularly due to their potential to generate sparse representations of data based on their morphological diversity. We here consider a scenario of image denoising using an overcomplete dictionary of sparse linear transforms. Rather than using the basic approach where the denoised image is obtained by simple averaging of denoised estimates provided by each sparse transform, we here develop an elegant Bayesian framework to optimally combine the individual estimates. Our derivation of the optimally combined denoiser relies on a scale mixture of Gaussian (SMG) prior on the coefficients in each representation transform. Exploiting this prior, we design a Bayesian ℓ2-risk (mean field) nonlinear estimator and we derive a closed-form for its expression when the SMG specializes to the Bessel K form prior. Experimental results are carried out to show the striking profits gained from exploiting sparsity of data and their morphological diversity.

Using multiple uncertain examples and adaptative fuzzy reasoning to optimize image characterization

This article proposes an automatic characterization method by comparing unknown images with examples more or less known. Our approach allows to use uncertain examples but easy to obtain (e.g. by automatic retrieval on the Internet). The use of fuzzy logic and adaptive clustering makes it possible to reduce automatically the noise from this database by preserving only the examples having a strong level of redundancy in the dominant shapes. To validate this method, we compared our artificial process of recognition with the estimation of human operators. The tests show that the automatic process gives an average accuracy of the characterization near to 95%.

Multivariate statistical modeling of images in sparse multiscale transforms domain

In this paper, we propose a multivariate statistical model to characterize the inter- and intra-scale dependencies between image coefficients in the oriented and non-oriented sparse multiscale transforms domain. Our proposed model, namely the Multivariate Bessel K Form, is based on multivariate extension of Bessel K Form distribution. To establish this model in practice, we propose an analytical form of PDF and then estimate its hyperparameters. Also, we compared it to the other models proposed in literature such as the Anisotropic Multivariate Generalized Gaussian and the Jeffrey models, in order to demonstrate its capabilities to capture the inter- and intra-scale dependencies between image detail coefficients.

Bayesian denoising based on the MAP estimation in wavelet-domain using Bessel K form prior

In this paper, a nonparametric Bayesian estimator in the wavelet domain using the Bessel K form (BKF) distribution will be presented. Our first contribution is to show how the BKF prior is suited to characterize images belonging to Besov spaces. Exploiting this prior, our second contribution is to design a Bayesian L/sub 1/-loss maximum a posteriori estimator nonlinear denoiser, for which we formally establish the mathematical properties. Finally, a comparative study is carried to show the effectiveness of our Bayesian denoiser compared to other denoising approaches.