Hassan Fenniri

A robust algorithm for convolutive blind source separation in presence of noise

We consider the blind source separation (BSS) problem in the noisy context. We propose a new methodology in order to enhance separation performances in terms of efficiency and robustness. Our approach consists in denoising the observed signals through the minimization of their total variation, and then minimizing divergence separation criteria combined with the total variation of the estimated source signals. We show by the way that the method leads to some projection problems that are solved by means of projected gradient algorithms. The efficiency and robustness of the proposed algorithm using Hellinger divergence are illustrated and compared with the classical mutual information approach through numerical simulations.

Fast communication: New blind source separation method of independent/dependent sources

We introduce a new blind source separation approach, based on modified Kullback-Leibler divergence between copula densities, for both independent and dependent source component signals. In the classical case of independent source components, the proposed method generalizes the mutual information (between probability densities) procedure. Moreover, it has the great advantage to be naturally extensible to separate mixtures of dependent source components. Simulation results are presented showing the convergence and the efficiency of the proposed algorithms.

On convolutive Blind Source Separation in a noisy context and a total variation regularization

We propose a new strategy for improving classical Blind Source Separation (BSS) methods. This strategy consists in denoising both the observed and the estimated source signals, and is based on the minimization of a regularized criterion which takes into account the Total Variation of the signal. We prove by the way that the method leads to a projection problem which is solved by means of projected gradient algorithm. The effectiveness and the robustness of the proposed separating process are shown on numerical examples.

Blind noisy mixture separation for independent/dependent sources through a regularized criterion on copulas

The paper introduces a new method for Blind Source Separation (BSS) in noisy instantaneous mixtures of both independent or dependent source component signals. This approach is based on the minimization of a regularized criterion. Precisely, it consists in combining the total variation method for denoising with the Kullback-Leibler divergence between copula densities. The latter takes advantage of the copula to model the structure of the dependence between signal components. The obtained algorithm achieves separation in a noisy context where standard BSS methods fail. The efficiency and robustness of the proposed approach are illustrated by numerical simulations. HighlightsThe paper provides a new Blind source separation for noisy mixtures of independent/dependent sources.The proposed approach combine TV-regularization for denoising and separation by minimizing TV-regularized Kullback-Leibler divergence between copulas.The efficiency and robustness properties of the proposed approach have been illustrated by simulations.

A new criterion for second order cyclostationary blind source separation

In this paper, we propose a new blind separation criterion for second order cyclostationary sources with known and different cyclic frequencies. The method results from the spectral analysis; it is based on the use of the second order cyclostationary characteristics of the source signals. The theoretical results are presented and proved. The computer simulations show a good performance of the proposed method in comparison with Sobi, CycloSobi and Jade algorithms.

Selection of discriminant mid-infrared wavenumbers by combining a naïve Bayesian classifier and a genetic algorithm: Application to the evaluation of lignocellulosic biomass biodegradation

Infrared spectroscopy provides useful information on the molecular compositions of biological systems related to molecular vibrations, overtones, and combinations of fundamental vibrations. Mid-infrared (MIR) spectroscopy is sensitive to organic and mineral components and has attracted growing interest in the development of biomarkers related to intrinsic characteristics of lignocellulose biomass. However, not all spectral information is valuable for biomarker construction or for applying analysis methods such as classification. Better processing and interpretation can be achieved by identifying discriminating wavenumbers. The selection of wavenumbers has been addressed through several variable- or feature-selection methods. Some of them have not been adapted for use in large data sets or are difficult to tune, and others require additional information, such as concentrations. This paper proposes a new approach by combining a naïve Bayesian classifier with a genetic algorithm to identify discriminating spectral wavenumbers. The genetic algorithm uses a linear combination of an a posteriori probability and the Bayes error rate as the fitness function for optimization. Such a function allows the improvement of both the compactness and the separation of classes. This approach was tested to classify a small set of maize roots in soil according to their biodegradation process based on their MIR spectra. The results show that this optimization method allows better discrimination of the biodegradation process, compared with using the information of the entire MIR spectrum, the use of the spectral information at wavenumbers selected by a genetic algorithm based on a classical validity index or the use of the spectral information selected by combining a genetic algorithm with other methods, such as Linear Discriminant Analysis. The proposed method selects wavenumbers that correspond to principal vibrations of chemical functional groups of compounds that undergo degradation/conversion during the biodegradation of lignocellulosic biomass.

Features' selection based on weighted distance minimization, application to biodegradation process evaluation

Infrared spectroscopy can provide useful information of the biomass composition and has been extensively used in several domains such as biology, food science, pharmaceutical, petrochemical, agricultural applications, etc. However, not all spectral information are valuable for biomarkers construction or for applying regression or classification models and by identifying interesting wavenumbers a better processing and interpretation can be achieved. The selection of optimal subsets has been addressed through several variable or feature selection methods including genetic algorithms. Some of them are not adapted on large data, others require additional information such as concentrations or are difficult to tune. This paper proposes an alternative approach by considering a weighted Euclidean distance. We show on real Mid-infrared spectra that this constrained nonlinear optimizer allows identifying the wavenumbers that best highlights the discrimination within the periods of the biodegradation process of the ligno-cellulosic biomass. These results are compared with previous ones obtained by a genetic algorithm.