Blind Identification of Underdetermined Mixtures Based on the Hexacovariance and Higher-Order Cyclostationarity

International audienceIn this work, we consider the problem of blind identification of underdetermined mixtures in a cyclostationary context relying on sixth-order statistics. We propose to exploit the cyclostationarity at higher orders by taking into account the knowledge of source cyclic frequencies in the sample estimator of the observation hexacovariance. Two blind identification algorithms based on the proposed estimator are considered and their performances are tested by means of computer simulations. Our simulation results show that significant improvements can be obtained when both second and fourth-order cyclo-stationarities are exploited

Joint Analysis of Multiple Datasets by Cross-Cumulant Tensor (Block) Diagonalization

International audienceIn this paper, we propose approximate diagonalization of a cross-cumulant tensor as a means to achieve independent component analysis (ICA) in several linked datasets. This approach generalizes existing cumulant-based independent vector analysis (IVA). It leads to uniqueness, identifiability and resilience to noise that exceed those in the literature, in certain scenarios. The proposed method can achieve blind identification of underdetermined mixtures when single-dataset cumulant-based methods that use the same order of statistics fall short. In addition, it is possible to analyse more than two datasets in a single tensor factorization. The proposed approach readily extends to independent subspace analysis (ISA), by tensor block-diagonalization. The proposed approach can be used as-is or as an ingredient in various data fusion frameworks, using coupled decompositions. The core idea can be used to generalize existing ICA methods from one dataset to an ensemble

Blind identification of underdetermined mixtures of complex sources based on the characteristic function

International audienceIn this work we consider the problem of blind identification of underdetermined mixtures using the generating function of the observations. This approach had been successfully applied on real sources but had not been extended to the more attractive case of complex mixtures of complex sources. This is the main goal of the present study. By developing the core equation in the complex case, we arrive at a particular tensor stowage which involves an original tensor decomposition. Exploiting this decomposition, an algorithm is proposed to blindly estimate the mixing matrix. Three versions of this algorithm based on 2nd, 3rd and 4th-order derivatives of the generating function are evaluated on complex mixtures of 4-QAM and 8-PSK sources and compared to the 6-BIOME algorithm by means of simulation results

Blind source separation using statistical nonnegative matrix factorization

PhD ThesisBlind Source Separation (BSS) attempts to automatically extract and track a signal of interest in real world scenarios with other signals present. BSS addresses the problem of recovering the original signals from an observed mixture without relying on training knowledge. This research studied three novel approaches for solving the BSS problem based on the extensions of non-negative matrix factorization model and the sparsity regularization methods. 1) A framework of amalgamating pruning and Bayesian regularized cluster nonnegative tensor factorization with Itakura-Saito divergence for separating sources mixed in a stereo channel format: The sparse regularization term was adaptively tuned using a hierarchical Bayesian approach to yield the desired sparse decomposition. The modified Gaussian prior was formulated to express the correlation between different basis vectors. This algorithm automatically detected the optimal number of latent components of the individual source. 2) Factorization for single-channel BSS which decomposes an information-bearing matrix into complex of factor matrices that represent the spectral dictionary and temporal codes: A variational Bayesian approach was developed for computing the sparsity parameters for optimizing the matrix factorization. This approach combined the advantages of both complex matrix factorization (CMF) and variational -sparse analysis. BLIND SOURCE SEPARATION USING STATISTICAL NONNEGATIVE MATRIX FACTORIZATION ii 3) An imitated-stereo mixture model developed by weighting and time-shifting the original single-channel mixture where source signals can be modelled by the AR processes. The proposed mixing mixture is analogous to a stereo signal created by two microphones with one being real and another virtual. The imitated-stereo mixture employed the nonnegative tensor factorization for separating the observed mixture. The separability analysis of the imitated-stereo mixture was derived using Wiener masking. All algorithms were tested with real audio signals. Performance of source separation was assessed by measuring the distortion between original source and the estimated one according to the signal-to-distortion (SDR) ratio. The experimental results demonstrate that the proposed uninformed audio separation algorithms have surpassed among the conventional BSS methods; i.e. IS-cNTF, SNMF and CMF methods, with average SDR improvement in the ranges from 2.6dB to 6.4dB per source.Payap Universit

Blind source separation of underdetermined mixtures of event-related sources

International audienceThis paper addresses the problem of blind source separation for underdetermined mixtures (i.e., more sources than sensors) of event-related sources that include quasi-periodic sources (e.g., electrocardiogram (ECG)), sources with synchronized trials (e.g., event-related potentials (ERP)), and amplitude-variant sources. The proposed method is based on two steps: (i) tensor decomposition for underdetermined source separation and (ii) signal extraction by Kalman filtering to recover the source dynamics. A tensor is constructed for each source by synchronizing on the ''event'' period of the corresponding signal and stacking different periods along the second dimension of the tensor. To cope with the interference from other sources that impede on the extraction of weak signals, two robust tensor decomposition methods are proposed and compared. Then, the state parameters used within a nonlinear dynamic model for the extraction of event-related sources from noisy mixtures are estimated from the loading matrices provided by the first step. The influence of different parameters on the robustness to outliers of the proposed method is examined by numerical simulations. Applied to clinical electroencephalogram (EEG), ECG and magnetocardiogram (MCG), the proposed method exhibits a significantly higher performance in terms of expected signal shape than classical source separation methods such as piCA and FastICA

Joint Tensor Factorization and Outlying Slab Suppression with Applications

We consider factoring low-rank tensors in the presence of outlying slabs. This problem is important in practice, because data collected in many real-world applications, such as speech, fluorescence, and some social network data, fit this paradigm. Prior work tackles this problem by iteratively selecting a fixed number of slabs and fitting, a procedure which may not converge. We formulate this problem from a group-sparsity promoting point of view, and propose an alternating optimization framework to handle the corresponding $\ell_p$ ($0<p\leq 1$) minimization-based low-rank tensor factorization problem. The proposed algorithm features a similar per-iteration complexity as the plain trilinear alternating least squares (TALS) algorithm. Convergence of the proposed algorithm is also easy to analyze under the framework of alternating optimization and its variants. In addition, regularization and constraints can be easily incorporated to make use of \emph{a priori} information on the latent loading factors. Simulations and real data experiments on blind speech separation, fluorescence data analysis, and social network mining are used to showcase the effectiveness of the proposed algorithm