Mahieddine M. Ichir

Hidden Markov models for wavelet-based blind source separation

In this paper, we consider the problem of blind source separation in the wavelet domain. We propose a Bayesian estimation framework for the problem where different models of the wavelet coefficients are considered: the independent Gaussian mixture model, the hidden Markov tree model, and the contextual hidden Markov field model. For each of the three models, we give expressions of the posterior laws and propose appropriate Markov chain Monte Carlo algorithms in order to perform unsupervised joint blind separation of the sources and estimation of the mixing matrix and hyper parameters of the problem. Indeed, in order to achieve an efficient joint separation and denoising procedures in the case of high noise level in the data, a slight modification of the exposed models is presented: the Bernoulli-Gaussian mixture model, which is equivalent to a hard thresholding rule in denoising problems. A number of simulations are presented in order to highlight the performances of the aforementioned approach: 1) in both high and low signal-to-noise ratios and 2) comparing the results with respect to the choice of the wavelet basis decomposition.

Wavelet-Based Semiblind Channel Estimation for Ultrawideband OFDM Systems

Ultrawideband (UWB) communications involve very sparse channels, because the bandwidth increase results in a better time resolution. This property is used in this paper to propose an efficient algorithm that jointly estimates the channel and the transmitted symbols. More precisely, this paper introduces an expectation-maximization (EM) algorithm within a wavelet-domain Bayesian framework for semiblind channel estimation of multiband orthogonal frequency division multiplexing based UWB communications. A prior distribution is chosen for the wavelet coefficients of the unknown channel impulse response to model a sparseness property of the wavelet representation. This prior yields, in maximum a posteriori estimation, a thresholding rule within the EM algorithm. We particularly focus on reducing the number of estimated parameters by iteratively discarding ldquoinsignificantrdquo wavelet coefficients from the estimation process. Simulation results using UWB channels that were issued from both models and measurements show that, under sparseness conditions, the proposed algorithm outperforms pilot-based channel estimation in terms of the mean square error (MSE) and bit error rate (BER). Moreover, the estimation accuracy is improved, whereas the computational complexity is reduced compared with traditional semiblind methods.

Ultra wideband OFDM channel estimation through a wavelet based EM-MAP algorithm†

SUMMARY Ultra wideband (UWB) communications involve very sparse channels, since the bandwidth increase results in a better time resolution. This property is used here to propose an efficient algorithm jointly estimating the channel and the transmitted symbols. More precisely, this paper introduces an expectation-maximisation (EM) algorithm within a wavelet domain Bayesian framework for semi-blind channel estimation of multiband orthogonal frequency-division multiplexing (MB-OFDM) based UWB communications. A prior distribution is chosen for the wavelet coefficients of the unknown channel impulse response (CIR) in order to model a sparseness property of the wavelet representation. This prior yields, in maximum a posteriori (MAP) estimation, a thresholding rule within the EM algorithm. We particularly focus on reducing the number of estimated parameters by iteratively discarding ‘insignificant’ wavelet coefficients from the estimation process. Simulation results using UWB channels issued from both models and measurements show that under sparsity conditions, the proposed algorithm outperforms pilot based channel estimation in terms of mean square error (MSE) and bit error rate (BER). Moreover, the estimation accuracy is improved, while the computational complexity is reduced, when compared to traditional semi-blind methods. Copyright

Wavelet Domain Image Separation

In this paper, we consider the problem of blind signal and image separation using a sparse representation of the images in the wavelet domain. We consider the problem in a Bayesian estimation framework using the fact that the distribution of the wavelet coefficients of real world images can naturally be modeled by an exponential power probability density function. The Bayesian approach which has been used with success in blind source separation gives also the possibility of including any prior information we may have on the mixing matrix elements as well as on the hyperparameters (parameters of the prior laws of the noise and the sources). We consider two cases: first the case where the wavelet coefficients are assumed to be i.i.d. and second the case where we model the correlation between the coefficients of two adjacent scales by a first order Markov chain. This paper only reports on the first case, the second case results will be reported in a near future The estimation computations are done via a Monte Carlo Markov Chain (MCMC) procedure. Some simulations show the performances of the proposed method.

Hidden Markov models for wavelet image separation and denoising

In this paper, we consider the problem of blind source separation of 2D images under a Bayesian formulation (Bayes-BSS). We transport the problem to the wavelet domain to be able to define appropriate prior distributions for the wavelet coefficients of the unobservable sources: an independent Gaussians mixture (IGM) model, a hidden Markov tree (HMT) model and contextual hidden Markov field (CHMF) model. Indeed, we consider a limiting case of the aforementioned prior models to propose a simple procedure for joint source separation and denoising. This procedure shows to be efficient, especially for highly noisy observations. Simulation examples and comparisons with standard classical methods are presented to show the performances of the proposed approach.

Bayesian Blind Source Separation of Positive Non Stationary Sources

In this contribution, we address the problem of blind non negative source separation. This problem finds its application in many fields of data analysis. We propose herein a novel approach based on Gamma mixture probability priors: Gamma densities to constraint the unobserved sources to lie on the positive half plane; a mixture density with a first order Markov model on the associated hidden variables to account for eventual non stationarity on the sources. Posterior mean estimates are obtained via appropriate Monte Carlo Markov Chain sampling.

Bayesian Wavelet Based Signal and Image Separation

In this contribution, we consider the problem of blind source separation in a Bayesian estimation framework. The wavelet representation allows us to assign an adequate prior distribution to the wavelet coefficients of the sources. MCMC algorithms are implemented to test the validity of the proposed approach, and the non linear approximation of the wavelet transform is exploited to aleviate the algorithm.