### Learning Hidden Markov Sparse Models

"... This paper considers the problem of separating streams of unknown non-stationary signals from underdetermined mixtures of sources. The source signals are modeled as a hidden Markov model (HMM) where each state in the Markov chain is determined by a set of on (i.e., active) or off (i.e., inactive) st ..."

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This paper considers the problem of separating streams of unknown non-stationary signals from underdetermined mixtures of sources. The source signals are modeled as a hidden Markov model (HMM) where each state in the Markov chain is determined by a set of on (i.e., active) or off (i.e., inactive) states of the sources, with some unknown probability density functions (pdfs) in the on-state. Under the assumption that the number of active sources is small compared to the total number of sources (thus the sources are sparse), the goal is to recursively estimate the HMM state and the overcomplete mixing matrix (subsequently the source signals) for signal recovery. The proposed approach combines the techniques of HMM-based filtering and manifold-based dictionary learning for estimating both the state and the mixing matrix. Specifically, we model the on/off state of the source signals as a hidden Markov model. In particular, we consider only a sparse set of simultaneously active sources. Thus, this setting generalizes the typical scenario considered in dictionary learning in which there is a sparse number of temporally independent active signals. To extract the activity profile of the sources from the observations, a technique known as change-of-measure is used to decouple the observations from the sources by introducing a new probability measure over the set of observations. Under this new measure, the un-normalized conditional densities of the state and the transition matrix of the Markov chain can be computed recursively. Due to the scaling ambiguity of the mixing matrix, we introduce an equivalence relation, which partitions the set of mixing matrices into a set of equivalence classes. Rather than estimating the mixing matrix by imposing the unitnorm constraint, the proposed algorithm searches directly for an equivalence class that contains the true mixing matrix. In our simulations, the proposed recursive algorithm with manifoldbased dictionary learning, compared to algorithms with unitnorm constraint, estimates the mixing matrix more efficiently while maintaining high accuracy.

### Removal of Embedded Artefacts in ECG Signals by Independent Component Analysis

"... Abstract: Routinely recorded Electrocardiograms (ECGs) are often corrupted by artefacts; these artefacts make the visual interpretation and analysis of the ECG signal difficult. This paper presents a model, dynamic in structure, sufficiently suitable for removing the ECG artefacts caused by embedded ..."

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Abstract: Routinely recorded Electrocardiograms (ECGs) are often corrupted by artefacts; these artefacts make the visual interpretation and analysis of the ECG signal difficult. This paper presents a model, dynamic in structure, sufficiently suitable for removing the ECG artefacts caused by embedded objects in the body using independent component analysis technique. By simulation, the model is able to detect and remove extraneous noises in the conductive paths and discern essential nodes of ECG that are useful to clinicians. Our study, also demonstrates that convolutive ICA can be regarded as a useful tool for accurately estimating the effects of embedded object in the patients on ECG signals.

### Author manuscript, published in "N/P" DOI: 10.1016/j.clinph.2008.09.007 On the Blind Source Separation of Human Electroencephalogram by Approximate Joint Diagonalization of Second Order Statistics

"... helpful comments and suggestions about this paper. BSS of Human EEG by SOS AJD – Congedo et al. 2008 Over the last ten years blind source separation (BSS) has become a prominent processing tool in the study of human electroencephalography (EEG). Without relying on head modeling BSS aims at estimatin ..."

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helpful comments and suggestions about this paper. BSS of Human EEG by SOS AJD – Congedo et al. 2008 Over the last ten years blind source separation (BSS) has become a prominent processing tool in the study of human electroencephalography (EEG). Without relying on head modeling BSS aims at estimating both the waveform and the scalp spatial pattern of the intracranial dipolar current responsible of the observed EEG. In this review we begin by placing the BSS linear instantaneous model of EEG within the framework of brain volume conduction theory. We then review the concept and current practice of BSS based on second-order statistics (SOS) and on higher-order statistics (HOS), the latter better known as independent component analysis (ICA). Using neurophysiological

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"... www.elsevier.com/locate/dsp Second-order statistics based blind source separation using a bank of subband filters R.R. Gharieb a,b, ∗ and A. Cichocki a,c ..."

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www.elsevier.com/locate/dsp Second-order statistics based blind source separation using a bank of subband filters R.R. Gharieb a,b, ∗ and A. Cichocki a,c

### Neurocomputing 69 (2006) 497--522

, 2005

"... Multidimensional proton nuclear magnetic resonance spectra of biomolecules dissolved in aqueous solutions are usually contaminated by an intense water artifact. We discuss the application of a generalized eigenvalue decomposition (GEVD) method using a matrix pencil to solve the blind source separati ..."

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Multidimensional proton nuclear magnetic resonance spectra of biomolecules dissolved in aqueous solutions are usually contaminated by an intense water artifact. We discuss the application of a generalized eigenvalue decomposition (GEVD) method using a matrix pencil to solve the blind source separation (BSS) problem of removing the intense solvent peak and related artifacts. The method explores correlation matrices of the signals and their filtered versions in the frequency domain and implements a two-step algebraic procedure to solve the GEVD. Two-dimensional nuclear Overhauser enhancement spectroscopy (2D NOESY) of dissolved proteins is studied. Results are compared to those obtained with the SOBI [Belouchrani et al., IEEE Trans. Signal Process. 45(2) (1997) 434--444] algorithm which jointly diagonalizes several time-delayed correlation matrices and to those of the fastICA [Hyva rinen www.elsevier.com/locate/neucom 0925-2312/$ - see front matter r 2005 Elsevier B.V. All rights reserved.

### A AID:461 Vol....(...)

, 2003

"... This paper presents a novel approach to blind source separation of narrowband signals in additive either white (i.e., time-uncorrelated) noise or colored (i.e., time-correlated) noise of which the frequencies of its spectral peaks are either known or can be estimated. The main idea behind this appro ..."

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This paper presents a novel approach to blind source separation of narrowband signals in additive either white (i.e., time-uncorrelated) noise or colored (i.e., time-correlated) noise of which the frequencies of its spectral peaks are either known or can be estimated. The main idea behind this approach is that a signal vector can be decomposed into a set of subband signal vectors in order to separate the spectra of the signals of interest from the noise spectra. It is shown that the subband technique can provide an unbiased estimate of the second-order statistics of a noisy observed signal vector. The proposed blind source separation algorithm is developed: (1) by whitening the noisy observed signal vector using the eigenvalue decomposition (EVD) of an unbiased estimate of the zero time-lag correlation matrix computed on the basis of the subband signals; and (2) by applying the joint approximate diagonalization (JAD) on a new proposed set of time-lag correlation matrices of the whitened signal vector. In this set, each correlation matrix of the whitened signal vector at certain time-lag is decomposed into a subset of the correlation matrices between the whitened signal vector and its subband vectors. This is motivated by the capability of separating and then omitting the crosscorrelation matrices belonging to the subbands of the colored noise from the set. Simulation results using computer-generated signals, real-world speech and real-world biomedical signals confirm the high efficiency and usefulness of the proposed approach.

### Instantaneous Blind Source Separation Based on the

, 2000

"... This paper provides insight into the algebraic and geometric structure of Instantaneous Blind Signal Separation based on the assumptions that the cross-correlation functions of the source signals are zero and that the source auto-correlation functions are linearly independent. The presented viewpoin ..."

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This paper provides insight into the algebraic and geometric structure of Instantaneous Blind Signal Separation based on the assumptions that the cross-correlation functions of the source signals are zero and that the source auto-correlation functions are linearly independent. The presented viewpoint is unifying in the sense that all kinds of statistical variability in the data, such as temporal correlations and nonstationarity, are exploited in the same way. A new method for solving the IBSS problem is presented that is based on the generalized eigenvalue decomposition. Keywords--- Instantaneous blind source separation, homogeneous multivariate polynomials, nonstationarity, coloredness.

### ANALYSIS OF MAX-MIN EIGENVALUE OF CONSTRAINED LINEAR COMBINATIONS OF SYMMETRIC MATRICES

"... This paper studies the problem whether the smallest eigenvalue of constrained linear combinations of symmetric matrices can reach a desirable value, which actually extends the mathematical problem of finding a Positive Definite Linear Combination of symmetric matrices(PDLC), and provides a universal ..."

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This paper studies the problem whether the smallest eigenvalue of constrained linear combinations of symmetric matrices can reach a desirable value, which actually extends the mathematical problem of finding a Positive Definite Linear Combination of symmetric matrices(PDLC), and provides a universal framework to maximize the minimal eigenvalue of linear combined symmetric matrices. For solving this problem, we cast an equivalent optimization task, and propose one general algorithm framework that is proved to be globally optimal and convergent. Both theoretical analysis and experiments under a typical constraint verify our algorithm’s validity and efficiency. Index Terms — Matrix multiplication, Optimization methods, Spectral analysis, Eigenvalues and eigenfunctions

### Avenue de la Forêt de Haye F-54516 Vandoeuvre-les-Nancy

"... Blind source separation, wavelet denoising and discriminant analysis for EEG artefacts and noise cancelling ..."

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Blind source separation, wavelet denoising and discriminant analysis for EEG artefacts and noise cancelling