Sparse Blind Source Separation Research Articles

Blind separation of sparse sources from nonlinear mixtures

Blind source separation (BSS) has been studied well when the sources are sparse signals and their combinations are linear. Sparse component analysis (SCA) or dictionary learning algorithms propose well-known approaches for performing BSS in this model. In this study, we explore BSS when the sources are sparse signals, however, their combinations are nonlinear. The considered scenario can be adapted to several signal processing applications such as machine learning and system identification. To perform BSS, we first approximate the nonlinear mixture functions with the polynomial functions. Then, using an alternating approach, we estimate the sources and the coefficients of polynomial functions. The considered strategy is similar to one employed in dictionary learning algorithms for sparse representation of signals. In fact, in iterations where the sources are estimated, we cluster the signals, and in iterations where the coefficients of polynomial functions are estimated, we assign a polynomial manifold to each cluster. The identifiability issues of the considered nonlinear model are also discussed. Experimental results demonstrate the effectiveness of the proposed method relative to state-of-the-art methods.

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

Sparse Blind Source Separation (sBSS) plays a key role in scientific domains as different as biomedical imaging, remote sensing or astrophysics. Such fields however require the development of increasingly faster and scalable BSS methods without sacrificing the separation performances. To that end, we introduce in this work a new distributed sparse BSS algorithm based on a mini-batch extension of the Generalized Morphological Component Analysis algorithm (GMCA). Precisely, it combines a robust projected alternated least-squares method with mini-batch optimization. The originality further lies in the use of a manifold-based aggregation of the asynchronously estimated mixing matrices. Numerical experiments are carried out on realistic spectroscopic spectra, and highlight the ability of the proposed distributed GMCA (dGMCA) to provide very good separation results even when very small mini-batches are used. Quite unexpectedly, the algorithm can further outperform the (non-distributed) state-of-the-art methods for highly sparse sources.

Sequential Sparse Blind Source Separation for Non-Linear Mixtures

Linear Blind Source Separation (BSS) has known a tremendous success in fields ranging from biomedical imaging to astrophysics. In this work, we however propose to depart from the usual linear setting and tackle the case in which the sources are mixed by an unknown non-linear function. We propose to use a sequential decomposition of the data enabling its approximation by a linear-by-part function. Beyond separating the sources, the introduced StackedAMCA can further empirically learn in some settings an approximation of the inverse of the unknown non-linear mixing, enabling to reconstruct the sources despite a severely ill- posed problem. The quality of the method is demonstrated experimentally, and a comparison is performed with state-of-the art non-linear BSS algorithms.

Sparse BSS from Poisson Measurements.

The problem of sparse Blind Source Separation (BSS) has been extensively studied when the noise is additive and Gaussian. This is however not the case when the measurements follow Poisson or shot noise statistics, which is customary with counting-based measurements. To that purpose, we introduce a novel sparse BSS algorithm coined pGMCA (poisson-Generalized Morphological Component Analysis) that specifically tackles the blind separation of sparse sources from measurements following Poisson statistics. The proposed algorithm builds upon Nesterov's smoothing technique to define a smooth approximation of sparse BSS, with a data fidelity term derived from the Poisson likelihood. This allows to design a block coordinate descent-based minimization procedure with a simple choice of the regularization parameter. Numerical experiments have been carried out that illustrate the robustness of the proposed method with respect to Poisson noise. The pGMCA algorithm has been further evaluated in a realistic astrophysical X-ray imaging setting.

Suppression Of Channel Interference In Optical Communication Networks Based On Blind Signal Separation

In order to overcome the problem of low accuracy and poor stability caused by the one-sided information blind separation analysis of the current communication channel interference suppression research methods, this paper proposes the optical communication network channel interference suppression method based on blind signal separation algorithm. The receiver unit, field programmable gate array (FPGA) unit, memory chip group and other modules are used to construct the channel signal acquisition system, and the collected signals are preprocessed by centralisation and whitening. Based on the signal preprocessing results, the blind separation of instantaneous linear mixed signals, blind separation of convolutional mixed signals and blind separation of sparse sources were comprehensively analysed to obtain the source signals and realise channel interference suppression of optical communication network. Experimental results show that this method has high interference precision, strong stability and good application prospect.

Suppression of channel interference in optical communication networks based on blind signal separation

In order to overcome the problem of low accuracy and poor stability caused by the one-sided information blind separation analysis of the current communication channel interference suppression research methods, this paper proposes the optical communication network channel interference suppression method based on blind signal separation algorithm. The receiver unit, field programmable gate array (FPGA) unit, memory chip group and other modules are used to construct the channel signal acquisition system, and the collected signals are preprocessed by centralisation and whitening. Based on the signal preprocessing results, the blind separation of instantaneous linear mixed signals, blind separation of convolutional mixed signals and blind separation of sparse sources were comprehensively analysed to obtain the source signals and realise channel interference suppression of optical communication network. Experimental results show that this method has high interference precision, strong stability and good application prospect.

Use of PALM for ℓ1 sparse matrix factorization: Difficulty and rationalization of a two-step approach

Blind Source Separation (BSS) is a key machine learning method, which has been successfully applied to analyze multichannel data in various domains ranging from medical imaging to astrophysics. Being an ill-posed matrix factorization problem, it is necessary to introduce extra regularizing priors on the sources. While using sparsity has led to improved factorization results, the quality of the separation process turns out to be dramatically dependent on the minimization strategy and the regularization parameters. In this scope, the Proximal Alternating Linearized Minimization (PALM) has recently attracted a lot of interest as a generic, fast and highly flexible algorithm. Using PALM for sparse BSS is theoretically well grounded, but getting good empirical results requires a fine tuning of the involved regularization parameters, which might be too computationally expensive with real-world large-scale data, therefore mandating automatic parameter choice strategies. In this article, we first investigate the empirical limitations of using the PALM algorithm to perform sparse BSS and we explain their origin. Based on this, we further study and justify an alternative two-step algorithmic framework combining PALM with a heuristic approach, namely the Generalized Morphological Component Analysis (GMCA). This method enables an automatic parameter choice for the PALM step. Numerical experiments with comparisons to standard algorithms are carried out on two realistic experiments in spectroscopy and astrophysics.

Efficient Sparse Blind Source Separation Algorithm for two- Channel Acoustic Noise Reduction

Recently, the acoustic noise reduction problem is treated by twochannel forward blind source separation (BSS) techniques combined with normalized least mean square algorithm (T-FNLMS). The TFNLMS algorithm shows good performances in two-channel convolutive dispersive mixture. In this paper, we propose new BSS structure based on the two-channel sparse normalized least mean square algorithm (TS-NLMS). The TS-NLMS algorithm is proposed exactly when the convolutive mixing system is characterized by sparse impulse responses. To confirm the good performance of this proposed algorithm, intensive experiments are done in acoustic noise reduction.

Heuristics For Efficient Sparse Blind Source Separation

Sparse Blind Source Separation (sparse BSS) is a key method to analyze multichannel data in fields ranging from medical imaging to astrophysics. However, since it relies on seeking the solution of a non-convex penalized matrix factorization problem, its performances largely depend on the optimization strategy. In this context, Proximal Alternating Linearized Minimization (PALM) has become a standard algorithm which, despite its theoretical grounding, generally provides poor practical separation results. In this work, we first investigate the origins of these limitations, which are shown to take their roots in the sensitivity to both the initialization and the regularization parameter choice. As an alternative, we propose a novel strategy that combines a heuristic approach with PALM. We show its relevance on realistic astrophysical data.

Blind separation of a large number of sparse sources

Abstract Blind Source Separation (BSS) is one of the major tools to analyze multispectral data with applications that range from astronomical to biomedical signal processing. Nevertheless, most BSS methods fail when the number of sources becomes large, typically exceeding a few tens. Since the ability to estimate large number of sources is paramount in a very wide range of applications, we introduce a new algorithm, coined block-Generalized Morphological Component Analysis (bGMCA) to specifically tackle sparse BSS problems when large number of sources need to be estimated. Sparse BSS being a challenging nonconvex inverse problem in nature, the role played by the algorithmic strategy is central, especially when many sources have to be estimated. For that purpose, the bGMCA algorithm builds upon block-coordinate descent with intermediate size blocks. Numerical experiments are provided that show the robustness of the bGMCA algorithm when the sources are numerous. Comparisons have been carried out on realistic simulations of spectroscopic data.

Blind separation of sparse sources in the presence of outliers

Blind Source Separation (BSS) plays a key role to analyze multichannel data since it aims at recovering unknown underlying elementary sources from observed linear mixtures in an unsupervised way. In a large number of applications, multichannel measurements contain corrupted entries, which are highly detrimental for most BSS techniques. In this article, we introduce a new robust BSS technique coined robust Adaptive Morphological Component Analysis (rAMCA). Based on sparse signal modeling, it makes profit of an alternate reweighting minimization technique that yields a robust estimation of the sources and the mixing matrix simultaneously with the removal of the spurious outliers. Numerical experiments are provided that illustrate the robustness of this new algorithm with respect to aberrant outliers on a wide range of blind separation instances. In contrast to current robust BSS methods, the rAMCA algorithm is shown to perform very well when the number of observations is close or equal to the number of sources.

Majorization–minimization for blind source separation of sparse sources

In this paper we propose the Majorization–Minimization Blind Spare Source Separation (MM-BSSS) algorithm for solving the blind source separation (BSS) problem when the source signals are known a priori to be sparse, or can be sparsely represented in some dictionary. The algorithm capitalizes on a previous result by Chartrand (2007 [24]) that shows certain classes of nonconvex functions perform better than the convex ℓ1-norm in measuring sparsity of a signal. In this paper we propose a majorization–minimization (MM) method for minimizing such a nonconvex objective function. The method can be simplified by choosing the non-convex function to be separable. In this paper we employ a previously developed technique (Mourad and Reilly, 2010 [26]) for constructing the MM surrogate function, which reduces the sparse BSS problem to an iterative computation of the minor eigenvectors of particular covariance matrices. These features permit a computationally efficient implementation. The proposed algorithm enjoys several advantages such as robustness to noise and the ability to estimate the number of source signals. Numerical results show that the proposed algorithm outperforms other well-known algorithms that solve the same problem.

A remote sensing image fusion method based on feedback sparse component analysis

We propose a new remote sensing image (RSI) fusion technique based on sparse blind source separation theory. Our method employs feedback sparse component analysis (FSCA), which can extract the original image in a step-by-step manner and is robust against noise. For RSIs from the China–Brazil Earth Resources Satellite, FSCA can separate useful surface feature information from redundant information and noise. The FSCA algorithm is therefore used to develop two RSI fusion schemes: one focuses on fusing high-resolution and multi-spectral images, while the other fuses synthetic aperture radar bands. The experimental results show that the proposed method can preserve spectral and spatial details of the source images. For certain evaluation indexes, our method performs better than classical fusion methods.

Estimation of input function from dynamic PET brain data using Bayesian blind source separation

Selection of regions of interest in an image sequence is a typical prerequisite step for estimation of time-activity curves in dynamic positron emission tomography (PET). This procedure is done manually by a human operator and therefore suffers from subjective errors. Another such problem is to estimate the input function. It can be measured from arterial blood or it can be searched for a vascular structure on the images which is hard to be done, unreliable, and often impossible. In this study, we focus on blind source separation methods with no needs of manual interaction. Recently, we developed sparse blind source separation and deconvolution (S-BSS-vecDC) method for separation of original sources from dynamic medical data based on probability modeling and Variational Bayes approximation methodology. In this paper, we extend this method and we apply the methods on dynamic brain PET data and application and comparison of derived algorithms with those of similar assumptions are given. The S-BSS-vecDC algorithm is publicly available for download.

Digital in-line particle holography: twin-image suppression using sparse blind source separation

We propose a robust autofocus method for reconstructing digital holograms and twin-image removal based on blind source separation approach. The method is made up of two components: an efficient quincunx lifting scheme based on wavelet packet transform, whose role is to maximize a sharpness metric related to the sparseness of the input holograms, and a geometric unmixing algorithm, which achieves the separation task. Experimental results confirm the ability of sparse blind source separation to discard the unwanted twin-image from in-line digital holograms of particles.

Decentralized modal identification of structures using parallel factor decomposition and sparse blind source separation

In this paper, a novel decentralized modal identification method is proposed utilizing the concepts of sparse blind source separation (BSS) and parallel factor decomposition. Unlike popular ambient modal identification methods which require large arrays of simultaneous vibration measurements, the decentralized algorithm presented here operates on partial measurements, utilizing a sub-set of sensors at-a-time. Mathematically, this leads to an underdetermined source separation problem, which is addressed using sparsifying wavelet transforms. The proposed method builds on a previously presented concept by the authors, which utilizes the stationary wavelet packet transform (SWPT) to generate an over-complete dictionary of sparse bases. However, the redundant SWPT can be computationally intensive depending on the bandwidth of the signals and the sampling frequency of the vibration measurements. This issue of computational burden is alleviated through a new method proposed here, which is based on a multi-linear algebra tool called PARAllel FACtor (PARAFAC) decomposition. At the core of this method, the wavelet packet decomposition coefficients are used to form a covariance tensor, followed by PARAFAC tensor decomposition to separate the modal responses. The underdetermined source identifiability of PARAFAC enables source separation in wavelet packet coefficients with considerable mode mixing, thereby relaxing the conditions to generate over-complete bases, thus reducing the computational burden. The proposed method is validated using a series of numerical simulations followed by an implementation on recorded ambient vibration measurements obtained from the UCLA factor building.

A decentralized blind source separation algorithm for ambient modal identification in the presence of narrowband disturbances

In this paper, a new decentralized identification method based on the principles of blind source separation (BSS) that can perform modal identification in the presence of narrowband external excitations is presented. This algorithm is based on the principle of sparse BSS involving wavelet transforms to undertake identification for underdetermined static mixtures. Most BSS methods in the context of modal identification assume that the excitation is white and does not contain narrow band excitation frequencies. However, this assumption is not satisfied in many situations when the excitation is a superposition of narrowband harmonic(s) and broadband disturbance, for example, rotating machinery fixed to flexible structures, human-induced vibration in pedestrian bridges, or dynamic interaction with surrounding structures. Under such conditions, traditional BSS methods (such as second-order blind identification) yield sources (modes) without any indication as to whether the identified source(s) is a system or an excitation harmonic. In the proposed method, underdetermined BSS is employed, involving transformation of measurements to the time–frequency domain, resulting in a sparse representation. The statistical characteristics of the sources are estimated using residual bootstrap technique, which are then used to delineate the sources corresponding to external disturbances versus intrinsic modes of the system, in a decentralized fashion. The decentralized architecture is aimed at reducing the cost of instrumentation in both traditional wired and recent wireless applications. The performance of the algorithm is demonstrated using both a numerical study and a bench-scale laboratory experiment. The primary advantage of the proposed method is its ability to identify the modal harmonics of a flexible structure under narrowband excitations, in a decentralized fashion, where traditional BSS algorithms fail to achieve the same goals. Copyright © 2013 John Wiley & Sons, Ltd.

Nonnegative Sparse Blind Source Separation for NMR Spectroscopy by Data Clustering, Model Reduction, and $\ell_1$ Minimization

Motivated by applications in nuclear magnetic resonance (NMR) spectroscopy, we introduce a novel blind source separation (BSS) approach to treat nonnegative and correlated data. We consider the (over)-determined case where $n$ sources are to be separated from $m$ linear mixtures ($m\geq n$). Among the $n$ source signals, there are $n-1$ partially overlapping (Po) sources and one positive everywhere (Pe) source. This condition is applicable for many real-world signals such as NMR spectra of urine and blood serum for metabolic fingerprinting and disease diagnosis. The geometric properties of the mixture matrix and the sparseness structure of the source signals (in a transformed domain) are crucial to the identification of the mixing matrix and the sources. The method first identifies the mixing coefficients of the Pe source by exploiting geometry in data clustering. Then subsequent elimination of variables leads to a sub-BSS problem of the Po sources solvable by the minimal cone method and related linear pr...

A Recursive Sparse Blind Source Separation Method and Its Application to Correlated Data in NMR Spectroscopy of Biofluids

Motivated by the nuclear magnetic resonance (NMR) spectroscopy of biofluids (urine and blood serum), we present a recursive blind source separation (rBSS) method for nonnegative and correlated data. BSS problem arises when one attempts to recover a set of source signals from a set of mixture signals without knowing the mixing process. Various approaches have been developed to solve BSS problems relying on the assumption of statistical independence of the source signals. However, signal independence is not guaranteed in many real-world data like the NMR spectra of chemical compounds. The rBSS method introduced in this paper deals with the nonnegative and correlated signals arising in NMR spectroscopy of biofluids. The statistical independence requirement is replaced by a constraint which requires dominant interval(s) from each source signal over some of the other source signals in a hierarchical manner. This condition is applicable for many real-world signals such as NMR spectra of urine and blood serum for metabolic fingerprinting and disease diagnosis. Exploiting the hierarchically dominant intervals from the source signals, the rBSS method reduces the BSS problem into a series of sub-BSS problems by a combination of data clustering, linear programming, and successive elimination of variables. Then in each sub-BSS problem, an ? 1 minimization problem is formulated for recovering the source signals in a sparse transformed domain. The method is substantiated by examples from NMR spectroscopy data and is promising towards separation and detection in complex chemical spectra without the expensive multi-dimensional NMR data.

Postprocessing and sparse blind source separation of positive and partially overlapped data

We study sparse blind source separation (BSS) for a class of positive and partially overlapped signals. The signals are only allowed to have nonoverlapping at certain locations, while they could overlap with each other elsewhere. For nonnegative data, a novel approach has been proposed by Naanaa and Nuzillard (NN) assuming that nonoverlapping exists for each source signal at some location of acquisition variable. However, the NN method introduces errors (spurious peaks) in the output when their nonoverlapping condition is not satisfied. To resolve this problem and improve robustness of separation, postprocessing techniques are developed in two aspects. One is to detect coherent and uncertain components from NN outputs by using multiple mixture data, then removing the uncertain portion to enhance signals. The other is to find better estimation of mixing matrix by leveraging reliable source peak structures in NN output. Numerical results on examples including NMR spectra of a 13C-1-acetylated carbohydrate with overlapping proton spin multiplets show satisfactory performance of the postprocessed sparse BSS and offer promise to resolve complex spectra without using multidimensional NMR methods.