Haut PDF Blind Source Separation: the Sparsity Revolution

Blind Source Separation: the Sparsity Revolution

Blind Source Separation: the Sparsity Revolution

Abstract Over the last few years, the development of multi-channel sensors motivated inter- est in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the so-called blind source separation (BSS) problem. In this context, as clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity. Recently, sparsity and morphological diversity have emerged as a novel and effective source of diversity for BSS. We give here some essential insights into the use of sparsity in source separation and we outline the essential role of morphological diversity as being a source of diversity or contrast between the sources. This paper overviews a sparsity-based BSS method coined General- ized Morphological Component Analysis (GMCA) that takes advantages of both morphological diversity and sparsity, using recent sparse overcomplete or redun- dant signal representations. GMCA is a fast and efficient blind source separation method. In remote sensing applications, the specificity of hyperspectral data should be accounted for. We extend the proposed GMCA framework to deal with hyper- spectral data. In a general framework, GMCA provides a basis for multivariate data analysis in the scope of a wide range of classical multivariate data restorate. Nu- merical results are given in color image denoising and inpainting. Finally, GMCA is applied to the simulated ESA/Planck data. It is shown to give effective astrophysical component separation.
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Damage Detection on the Champangshiehl Bridge using Blind Source Separation

Damage Detection on the Champangshiehl Bridge using Blind Source Separation

Figure 10. Damage detection results using EPCA. 6 CONCLUSION The philosophy pursued throughout this paper is to exploit experimental vibration measurements to ex- tract dynamic features of a system without resorting on modal identification results (i.e. natural frequen- cies and/or mode-shapes). To this purpose, tech- niques of the Blind Source Separation (BSS) family are considered and especially here, a variant of Prin- cipal Component Analysis based on the definition of Hankel matrices is used. In this method, the order (number of active principal components) is deter- mined by looking at the cumulated variance in the singular value diagram. Thus the problem of damage detection is tackled using the subspaces spanned by the active principal components. It consists in de- termining the angular coherence between subspaces obtained in current states with respect to a reference (healthy) state. The advantage of PCA over classical modal identification methods relies on its easiness of use. First results obtained on the Champangshiehl bridge are encouraging.
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Sparsity and adaptivity for the blind separation of partially correlated sources

Sparsity and adaptivity for the blind separation of partially correlated sources

partially correlated sources J. Bobin, J. Rapin, A. Larue and J-L Starck Abstract Blind source separation (BSS) is a very popular technique to analyze multichannel data. In this context, the data are modeled as the linear combination of sources to be retrieved. For that purpose, standard BSS methods all rely on some discrimination principle, whether it is statistical independence or morphological diversity, to distinguish between the sources. However, dealing with real-world data reveals that such assumptions are rarely valid in practice: the signals of interest are more likely partially correlated, which generally hampers the performances of standard BSS methods. In this article, we introduce a novel sparsity-enforcing BSS method coined Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve sparse and partially correlated sources. More precisely, it makes profit of an adaptive re-weighting scheme to favor/penalize samples based on their level of correlation. Extensive numerical experiments have been carried out which show that the proposed method is robust to the partial correlation of sources while standard BSS techniques fail. The AMCA algorithm is evaluated in the field of astrophysics for the separation of physical components from microwave data.
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Frequency Domain Blind Source Separation for Robot Audition Using a Parameterized Sparsity Criterion

Frequency Domain Blind Source Separation for Robot Audition Using a Parameterized Sparsity Criterion

source mixture is modeled as a convolutive mixture between the sources and the impulse responses of the different paths from the sources to the microphones. In this case, we have to find a separation filter according to the considered separation criterion. In the frequency domain, the convolutive mixture is approximated by an instantaneous one, and the problem becomes easier as we have to find a separation matrix in- stead of a separation filter. But this has to be done for each frequency bin which gives rise to the permutation and scale problem. Another advantage of the time-frequency domain is the sparsity of the signals in this domain. A signal is sparse when it is zero or nearly zero in most of its samples.
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An Unified Approach for Blind Source Separation Using Sparsity and Decorrelation

An Unified Approach for Blind Source Separation Using Sparsity and Decorrelation

Index Terms— Blind Source Separation; Sparsity; Inde- pendant Component Analysis; Optimization 1. INTRODUCTION The instantaneous linear mixture model of BSS assumes that: x = As + e , (1) where x ∈ R M ×T and s ∈ R N ×T are the matrices of mixture channels and source signals respectively. A ∈ R M ×N is the mixing matrix and e ∈ R M ×T models the background noise. The ICA [1] methods are often applied when M ≥ N (over-determined case). These methods try to achieve sep- aration by minimizing an independence criterion between the components of the estimated sources. In the under- determined case (M < N ), two-steps methods based on sparsity are largely used [2]: The mixing system is first es- timated using clustering methods [3], then the sources are estimated thanks to optimization approaches [4].
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From blind to guided audio source separation: How models and side information can improve the separation of sound

From blind to guided audio source separation: How models and side information can improve the separation of sound

Starting with blind separation of toy mixtures in the mid 90’s, research has pro- gressed up to real-world scenarios today, with applications to speech enhancement and recognition, music editing, 3D sound rendering, and audio information retrieval, among others. This has mostly been made possible by the development of increasingly informed separation techniques incorporating knowledge about the sources and/or the mixtures at hand. For instance, speech source separation for remote conferencing can benefit from prior knowledge of the room geometry and/or the names of the speakers, while music remastering will exploit instrument characteristics and knowledge of sound engineers mixing habits.
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Morphological diversity and sparsity in blind source separation

Morphological diversity and sparsity in blind source separation

jalal.fadili@greyc.ensicaen.fr - GREYC CNRS UMR 6072, Image Processing Group, ENSICAEN 14050, Caen Cedex, France Abstract. This paper describes a new blind source separation method for instantaneous linear mixtures. This new method coined GMCA (Gen- eralized Morphological Component Analysis) relies on morphological di- versity. It provides new insights on the use of sparsity for blind source separation in a noisy environment. GMCA takes advantage of the sparse representation of structured data in large overcomplete signal dictionar- ies to separate sources based on their morphology. In this paper, we define morphological diversity and focus on its ability to be a helpful source of diversity between the signals we wish to separate. We intro- duce the blind GMCA algorithm and we show that it leads to good re- sults in the overdetermined blind source separation problem from noisy mixtures. Both theoretical and algorithmic comparisons between mor- phological diversity and independence-based separation techniques are given. The effectiveness of the proposed scheme is confirmed in several numerical experiments.
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Séparation aveugle de sources en ingénierie biomédicale - Blind source separation in biomedical engineering

Séparation aveugle de sources en ingénierie biomédicale - Blind source separation in biomedical engineering

valeurs propres associées sont pour leur part égales, à une constante près, aux moments d’ordre quatre des sources. Deux ans plus tard nait la méthode FOOBI (Fourth Order Only Blind Identification) [26] qui sans blanchiment des observations permet d’identifier la matrice de mélange à partir du sous-espace signal d’ordre quatre. Cette méthode a récemment été améliorée par L. De Lathauwer et al. [49] en se servant notamment du procédé de diagonalisation conjointe. Les deux approches précédentes offrent l’avantage de permettre l’identification de mélanges sous-déterminés de sources (i.e. P > N ). En 1993 survient la méthode JADE (Joint Approximate Diagonalization of Eigen-matrices), au travers de laquelle J.-F. Cardoso et A. Souloumiac [30] présentent une solution algébrique à la maximization de leur contraste basé sur les cumulants d’ordre quatre. Ils étendent par la même occasion l’algorithme de Jacobi dans le but de diagonaliser conjointement un ensemble de matrices [31]. Ce dernier sera par la suite l’outil fard de nombreuses méthodes de SAS, et ce jusqu’à l’apogée des approches de décomposition tensorielle telle que PARAFAC [24]. En 1997, A. Ferréol et P. Chevalier [60] proposent une version de JADE, baptisée JADE cyclique, exploitant les éventuelles propriétés cyclostationnaires des signaux observés. Cette approche a pour intérêt d’être insensible à la présence d’un bruit de cohérence spatiale inconnue. Plus récemment, L. Albera et al. [1] mettent en oeuvre les méthodes ICAR (Independent Component Analysis using Redundancies) [3]–[5] et BIRTH (Blind Identification of mixtures of sources using Redundancies in the daTa Hexacovariance matrix) [2], [6], exploitant les redondances matricielles respectivement de la quadricovariance et de l’hexacovariance. Ces deux méthodes s’inscrivent au sein d’une même famille d’algorithmes baptisée BIOME (Blind Identification of Overcomplete Mixtures of sourcEs) [7]. En parallèle, A. Ferréol et al. étendent la méthode SOBI à l’ordre quatre sous le nom de FOBIUM (Fourth Order Blind Identification of Underdetermined Mixtures of sources) [58], [59]. Notons que les méthodes FOOBI, ICAR, BIRTH et FOBIUM ne nécessitent pas d’étape préalable de blanchiment et sont insensibles asymptotiquement à la présence d’un bruit de cohérence spatiale inconnue. En outre les algorithmes FOOBI, FOBIUM et BIRTH permettent de traiter des mélanges sous-déterminés de sources.
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Muscle artifact removal in ictal scalp-EEG based on blind source separation

Muscle artifact removal in ictal scalp-EEG based on blind source separation

IV. D ATASETS A. Generation of simulated data The main goal of this subsection is to explain how we ob- tain synthetic but realistic data for comparing the above BSS methods in the particular context of epileptic rapid ictal dis- charges. The simulated EEG data are generated using a realis- tic head and source model as described in [11]. 32−Channels EEG data were simulated from a single distributed source of 5cm 2 , referred to as "patch" in the following, located in the left superior temporal gyrus. Rapid ictal-like activities gen- erated by a neural mass model are assigned to the patch. 50 realizations of rapid ictal discharges simulations were gen- erated. These signals corresponded to "clean data". In order to generate noisy EEG simulations, 50 epochs of EEG mus- cle activity were extracted from real 32−channel EEG data. Each trial of EEG muscle activity was then normalized with respect to the channel showing the maximal power. Then, dif- ferent levels of amplitude of noisy background and muscular activities were added to the simulated rapid ictal discharges to get noisy simulated signals with different SNR values. B. Real data
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Faster and better sparse blind source separation through mini-batch optimization

Faster and better sparse blind source separation through mini-batch optimization

matrices with large condition numbers yield two major bottlenecks: i) an increased noise level in the source domain, and ii) the mixtures are closer to co-linearity, which makes the sources harder to distinguish. In these experiments, the noise level is fixed to 40 dB and the sparsity level is ρ = 0.1. The number of observations is set to 20, the number of sources to 5 and the number of samples per sources to 10000. Figure 3 shows the evolution of the mixing matrix criterion C A as a function of the mini-batch size t b for two values of the condition numbers: left panel 2.5 and right panel 7. As expected, the quality of the separation results of all methods decrease when the condition number increases. Similarly to the tests performed in the previous section, the dGMCA algorithm has better results for relatively small mini-batch sizes (but when the Fr´ echet mean is used, it eventually de- teriorates for t b < 25, cf. Fig. 3). The use of small batches along with the robust Fr´ echet mean leads to an improvement for t b < 25, which becomes more significant when the condition number increases up to a gain of about one order of magnitude. Similarly, when the mini-batch size decreases, the discrepancy between the two methods increases.
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An Improved Method of Permutation Correction in Convolutive Blind Source Separation

An Improved Method of Permutation Correction in Convolutive Blind Source Separation

1200 Montreal Road, Ottawa, Ontario, K1A 0R6, Canada (received June 7, 2010; accepted September 1, 2010 ) This paper proposes an improved method of solving the permutation problem inherent in frequency-domain of convolutive blind source separation (BSS). It com- bines a novel inter-frequency dependence measure: the power ratio of separated signals, and a simple but effective bin-wise permutation alignment scheme. The pro- posed method is easy to implement and surpasses the conventional ones. Simulations have shown that it can provide an almost ideal solution of the permutation problem for a case where two or three sources were mixed in a room with a reverberation time of 130 ms.
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Blind Source Separation for Robot Audition using Fixed Beamforming with HRTFs

Blind Source Separation for Robot Audition using Fixed Beamforming with HRTFs

Index Terms: blind source separation, beamforming, robot au- dition 1. Introduction Robot audition consists in the aptitude of an humanoid to under- stand its acoustic environment, separate and localize sources, identify speakers and recognize their emotions. This complex task is one of the target points of the R OMEO project [1]. This project aims to build an humanoid (R OMEO ) to help aged peo- ple in their everyday lives. In this project, we focus on blind source separation (BSS) using a microphone array (more than 2 sensors). In a blind source separation task, the separation should be done from the received microphone signals without prior knowledge of the mixing process. The only knowledge is limited to the array geometry. Source separation is the most im- portant step for human-robot interaction: it allows latter tasks like speakers identification, speech and motion recognition and environmental sound analysis.
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Underdetermined blind source separation of audio sources in time-frequency domain

Underdetermined blind source separation of audio sources in time-frequency domain

A challenging problem of BSS occurs when there are more sources than sensors, and this is referred to as underdeter- mined blind source separation (UBSS). A time-frequency based UBSS algorithm has been recently proposed in [2, 3] to suc- cessfully separate speech sources using time-frequency dis- tributions (TFDs). This algorithm provides good separation performance when the sources are disjoint in the TF plane. It also provides the separation of TF quasi-disjoint sources, that is the sources are allowed to have a small degree of overlap- ping in the TF plane. However, the intersection points in the TF plane are not directly treated. More precisely, a point at the intersection of two sources is clustered “randomly” to be- long to one of the sources. As a result, the source that picks up this point now contains some information from the other source while the later source loses some information of its own. However, for the other source, there is an interference
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Non-Negative Blind Source Separation Algorithm Based on Minimum Aperture Simplicial Cone

Non-Negative Blind Source Separation Algorithm Based on Minimum Aperture Simplicial Cone

Fig. 16. Four first elution profiles and corresponding mass spectra estimated by SCSA-UNS, from HPLC-LTQ Orbitrap data VIII. C ONCLUSION In this paper, we propose a geometrical method for separat- ing non-negative sources. The proposal, denoted SCSA-UNS, estimates the mixing matrix and the sources, by first reducing the dimension of the mixed data, followed by fitting a Min- imum Aperture Simplicial Cone (MASC) to the scatter plot of the dimension reduced data. SCSA-UNS does not require the independence of sources, neither their local dominance, but the positive orthant must be the unique MASC containing the scatter plot of the sources, to ensure recovering the true mixing matrix and the true sources. In noisy case, the proposed method starts by discarding the points most corrupted by the noise, which can significantly expand the scatter plot of mixed data, before looking for the MASC containing the data. Simulation on synthetic data have showned that the proposed method performs good separation for both independent and mutually correlated sources. The proposal has also been suc- cessfully used to estimate the pharmacokinetic compartments of [18F]-FDG tracer on human brain (in particular to estimated the Arterial Input Function) and to separate the elementary mass spectra of differents chemical compounds, from the mass spectra measured at the output of a liquid chromatograph.
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Nonlinear Blind Source Separation for Chemical Sensor Arrays Based on a Polynomial Representation

Nonlinear Blind Source Separation for Chemical Sensor Arrays Based on a Polynomial Representation

In the future, we would like to further analyze the theoretical stability of the problem in order to improve the selection of initial conditions for the algorithm. For the current version of the algorithm, the conditions are randomly selected and can sometimes lead to the algorithm not converging, in which case we restart the method until it succeeds. While this has not proven an issue for our current application (possibly due to the fact that the mixing coefficients are typically small), a more theoretical analysis would be important to avoid problems with more general mixing models, and possibly improve the accuracy and convergence speed of our proposed method.
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From Binaural to Multichannel Blind Source Separation using Fixed Beamforming with HRTFs

From Binaural to Multichannel Blind Source Separation using Fixed Beamforming with HRTFs

Z (f, k) = B (f ) X (f, k) (4) To design a fixed beamformer that will achieve the desired beam pattern (according to a desired direction response), the least-square (LS) technique is used [5] and thus the steering vectors are needed. In the case of robot audition, the microphones are often fixed in the head of the robot and it is generally hard to know exactly the ge- ometry of the microphone array (cf. figure 3). Besides, the phase and magnitude of the steering vectors do not take into account the influence of the head on the surrounding acoustic fields. So we pro- pose to use the Head Related Transfer Functions (HRTFs) as steering vectors {a (f, θ)} θ∈Θ , where Θ = {θ1 , . . . , θK} is a group of K a priori chosen steering directions (cf. figure 2). The HRTF charac- terizes how the signal emitted from a specific direction is received at a sensor fixed in a head. It takes into account the geometry of the head, and thus the geometry of the microphone array.
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Underdetermined Reverberant Blind Source Separation: Sparse Approaches for Multiplicative and Convolutive Narrowband Approximation

Underdetermined Reverberant Blind Source Separation: Sparse Approaches for Multiplicative and Convolutive Narrowband Approximation

Abstract—We consider the problem of blind source separa- tion for underdetermined convolutive mixtures. Based on the multiplicative narrowband approximation in the time-frequency domain with the help of Short-Time-Fourier-Transform (STFT) and the sparse representation of the source signals, we formulate the separation problem into an optimization framework. This framework is then generalized based on the recently investigated convolutive narrowband approximation and the statistics of the room impulse response. Algorithms with convergence proof are then employed to solve the proposed optimization problems. The evaluation of the proposed frameworks and algorithms for synthesized and live recorded mixtures are illustrated. The proposed approaches are also tested for mixtures with input noise. Numerical evaluations show the advantages of the proposed methods.
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ICAR, a tool for Blind Source Separation using Fourth Order Statistics only

ICAR, a tool for Blind Source Separation using Fourth Order Statistics only

VI. C ONCLUSION The ICAR algorithm, exploiting the information contained in the data statistics at fourth order only, has been proposed in this paper. This algorithm allows to process overdetermined (including square) mixtures of sources, provided the latter have marginal FO cumulants with the same sign, which is generally the case in radio communications contexts. Three conclusions can be drawn: first, in the presence of a Gaussian noise spatially and temporally white, the proposed method yields satisfactory results. Second, contrary to most BSS algorithms, the ICAR method is not sensitive to a Gaussian colored noise whose spatial coherence is unknown. Last, the ICAR algorithm is robust with respect to an over estimation of the number of sources, which is not the case for some methods such as JADE. Forthcoming works include the search for a contrast criterion associated with ICAR in order to analyse accurately its performance.
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Blind source separation methods applied to synthesized polysomnographic recordings: a comparative study

Blind source separation methods applied to synthesized polysomnographic recordings: a comparative study

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. HAL author manuscript inserm-00186093, version 1

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Combining superdirective beamforming and frequency-domain blind source separation for highly reverberant signals

Combining superdirective beamforming and frequency-domain blind source separation for highly reverberant signals

Received 14 January 2010; Accepted 1 June 2010 Academic Editor: Harvey Thornburg Copyright © 2010 Lin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Frequency-domain blind source separation (BSS) performs poorly in high reverberation because the independence assumption collapses at each frequency bins when the number of bins increases. To improve the separation result, this paper proposes a method which combines two techniques by using beamforming as a preprocessor of blind source separation. With the sound source locations supposed to be known, the mixed signals are dereverberated and enhanced by beamforming; then the beamformed signals are further separated by blind source separation. To implement the proposed method, a superdirective fixed beamformer is designed for beamforming, and an interfrequency dependence-based permutation alignment scheme is presented for frequency- domain blind source separation. With beamforming shortening mixing filters and reducing noise before blind source separation, the combined method works better in reverberation. The performance of the proposed method is investigated by separating up to 4 sources in different environments with reverberation time from 100 ms to 700 ms. Simulation results verify the outperformance of the proposed method over using beamforming or blind source separation alone. Analysis demonstrates that the proposed method is computationally efficient and appropriate for real-time processing.
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