Blind Source Separation Approach Research Articles

Blind Source Separation of Underdetermined Mixtures Based on Local Mean Decomposition and Conjugate Gradient Algorithm

Most of the existing underdetermined blind source separation (BSS) approaches assume that the source signals are strictly or partially sparse. This paper, however, presents a new BSS method in underdetermined mixing situation for non- sparse signals. The proposed method first introduces the local mean decomposition algorithm into the BSS problem to rebuild some extra mixing signals. Such signals are then combined with the initial mixtures such that the underdetermined BSS problem is transformed to a determined one and the difficulty of the deficiency of the mixtures is overcome. For the rebuilt mixtures and the newly formed determined BSS problem, the minimum mutual information principle is employed as the BSS cost function. A conjugate gradient learning algorithm is then derived for training the separating matrix. In each update step of the algorithm, the term of score function is estimated by a kernel function estimation algorithm. The simulation results have demonstrated the efficacy of the proposed underdetermined BSS method.  Index Terms—Blind source separation, underdetermined model, local mean decomposition, conjugate gradient

Efficient Source Separation Algorithms for Acoustic Fall Detection Using a Microsoft Kinect

Falls have become a common health problem among older adults. In previous study, we proposed an acoustic fall detection system (acoustic FADE) that employed a microphone array and beamforming to provide automatic fall detection. However, the previous acoustic FADE had difficulties in detecting the fall signal in environments where interference comes from the fall direction, the number of interferences exceeds FADE's ability to handle or a fall is occluded. To address these issues, in this paper, we propose two blind source separation (BSS) methods for extracting the fall signal out of the interferences to improve the fall classification task. We first propose the single-channel BSS by using nonnegative matrix factorization (NMF) to automatically decompose the mixture into a linear combination of several basis components. Based on the distinct patterns of the bases of falls, we identify them efficiently and then construct the interference free fall signal. Next, we extend the single-channel BSS to the multichannel case through a joint NMF over all channels followed by a delay-and-sum beamformer for additional ambient noise reduction. In our experiments, we used the Microsoft Kinect to collect the acoustic data in real-home environments. The results show that in environments with high interference and background noise levels, the fall detection performance is significantly improved using the proposed BSS approaches.

Nonstationary source separation using sequential and variational Bayesian learning.

Independent component analysis (ICA) is a popular approach for blind source separation where the mixing process is assumed to be unchanged with a fixed set of stationary source signals. However, the mixing system and source signals are nonstationary in real-world applications, e.g., the source signals may abruptly appear or disappear, the sources may be replaced by new ones or even moving by time. This paper presents an online learning algorithm for the Gaussian process (GP) and establishes a separation procedure in the presence of nonstationary and temporally correlated mixing coefficients and source signals. In this procedure, we capture the evolved statistics from sequential signals according to online Bayesian learning. The activity of nonstationary sources is reflected by an automatic relevance determination, which is incrementally estimated at each frame and continuously propagated to the next frame. We employ the GP to characterize the temporal structures of time-varying mixing coefficients and source signals. A variational Bayesian inference is developed to approximate the true posterior for estimating the nonstationary ICA parameters and for characterizing the activity of latent sources. The differences between this ICA method and the sequential Monte Carlo ICA are illustrated. In the experiments, the proposed algorithm outperforms the other ICA methods for the separation of audio signals in the presence of different nonstationary scenarios.

Uniqueness Analysis of Non-Unitary Matrix Joint Diagonalization

Matrix Joint Diagonalization (MJD) is a powerful approach for solving the Blind Source Separation (BSS) problem. It relies on the construction of matrices which are diagonalized by the unknown demixing matrix. Their joint diagonalizer serves as a correct estimate of this demixing matrix only if it is uniquely determined. Thus, a critical question is under what conditions is a joint diagonalizer unique. In the present work we fully answer this question about the identifiability of MJD based BSS approaches and provide a general result on uniqueness conditions of matrix joint diagonalization. It unifies all existing results which exploit the concepts of non-circularity, non-stationarity, non-whiteness, and non-Gaussianity. As a corollary, we propose a solution for complex BSS, which can be formulated in closed form in terms of an eigen and a singular value decomposition of two matrices.

PD-0495: Prediction of rectal bleeding in prostate cancer radiotherapy: blind source separation approaches

PD-0495: Prediction of rectal bleeding in prostate cancer radiotherapy: blind source separation approaches

Novel z-domain precoding method for blind separation of spatially correlated signals.

In this paper, we address the problem of blind separation of spatially correlated signals, which is encountered in some emerging applications, e.g., distributed wireless sensor networks and wireless surveillance systems. We preprocess the source signals in transmitters prior to transmission. Specifically, the source signals are first filtered by a set of properly designed precoders and then the coded signals are transmitted. On the receiving side, the Z-domain features of the precoders are exploited to separate the coded signals, from which the source signals are recovered. Based on the proposed precoders, a closed-form algorithm is derived to estimate the coded signals and the source signals. Unlike traditional blind source separation approaches, the proposed method does not require the source signals to be uncorrelated, sparse, or nonnegative. Compared with the existing precoder-based approach, the new method uses precoders with much lower order, which reduces the delay in data transmission and is easier to implement in practice.

Coronal Temperature Maps from Solar EUV Images: A Blind Source Separation Approach

Multi-wavelength solar images in the EUV are routinely used for analysing solar features such as coronal holes, filaments, and flares. However, images taken in different bands often look remarkably similar as each band receives contributions coming from regions with a range of different temperatures. This has motivated the search for empirical techniques that may unmix these contributions and concentrate salient morphological features of the corona in a smaller set of less redundant source images. Blind Source Separation (BSS) precisely does this. Here we show how this novel concept also provides new insight into the physics of the solar corona, using observations made by SDO/AIA. The source images are extracted using a Bayesian positive source separation technique. We show how observations made in six spectral bands, corresponding to optically thin emissions, can be reconstructed by linear combination of three sources. These sources have a narrower temperature response and allow for considerable data reduction since the pertinent information from all six bands can be condensed in only one single composite picture. In addition, they give access to empirical temperature maps of the corona. The limitations of the BSS technique and some applications are briefly discussed.

On the Convergence of Symmetrically Orthogonalized Bounded Component Analysis Algorithms for Uncorrelated Source Separation

Bounded Component Analysis (BCA) has recently been introduced as an alternative linear decomposition scheme. In this approach the boundedness property of sources is exploited to replace the usual independence assumption with a weaker assumption, which enables development of methods to separate both independent and dependent components from their mixtures. This paper positions total output range minimization based blind source separation approach as a BCA method for the separation of uncorrelated sources. It is shown that the global minimizers of the corresponding optimization problem are the perfect separators. Furthermore, a stationary point analysis for the corresponding algorithms based on symmetrical orthogonalization is provided. The main result of this analysis is that the range minimization based parallel BCA algorithm and the kurtosis maximization based Independent Component Analysis algorithm have related set of identified stationary points.

Blind vibration component separation and nonlinear feature extraction applied to the nonstationary vibration signals for the gearbox multi-fault diagnosis

Fault diagnosis of gearboxes, especially the gears and bearings, is of great importance to the long-term safe operation. An unexpected damage on the gearbox may break the whole transmission line down. It is therefore crucial for engineers and researchers to monitor the health condition of the gearbox in a timely manner to eliminate the impending faults. However, useful fault detection information is often submerged in heavy background noise. Thereby, a new fault detection method for gearboxes using the blind source separation (BSS) and nonlinear feature extraction techniques is presented in this paper. The nonstationary vibration signals were analyzed to reveal the operation state of the gearbox. The kernel independent component analysis (KICA) algorithm was used hereby as the BSS approach for the mixed observation signals of the gearbox vibration to discover the characteristic vibration source associated with the gearbox faults. Then the wavelet packet transform (WPT) and empirical mode decomposition (EMD) nonlinear analysis methods were employed to deal with the nonstationary vibrations to extract the original fault feature vector. Moreover, the locally linear embedding (LLE) algorithm was performed as the nonlinear feature reduction technique to attain distinct features from the feature vector. Lastly, the fuzzy k-nearest neighbor (FKNN) was applied to the fault pattern identification of the gearbox. Two case studies were carried out to evaluate the effectiveness of the proposed diagnostic approach. One is for the gear fault diagnosis, and the other is to diagnose the rolling bearing faults of the gearbox. The nonstationary vibration data was acquired from the gear and rolling bearing fault test-beds, respectively. The experimental test results show that sensitive fault features can be extracted after the KICA processing, and the proposed diagnostic system is effective for the multi-fault diagnosis of the gears and rolling bearings. In addition, the proposed method can achieve higher performance than that without KICA processing with respect to the classification rate.

Time-frequency approach to underdetermined blind source separation.

This paper presents a new time-frequency (TF) underdetermined blind source separation approach based on Wigner-Ville distribution (WVD) and Khatri-Rao product to separate N non-stationary sources from M(M <; N) mixtures. First, an improved method is proposed for estimating the mixing matrix, where the negative value of the auto WVD of the sources is fully considered. Then after extracting all the auto-term TF points, the auto WVD value of the sources at every auto-term TF point can be found out exactly with the proposed approach no matter how many active sources there are as long as N ≤ 2M-1. Further discussion about the extraction of auto-term TF points is made and finally the numerical simulation results are presented to show the superiority of the proposed algorithm by comparing it with the existing ones.

Blind source separation based on high-resolution time–frequency distributions

Blind source separation (BSS) based on time–frequency distributions (TFDs) exploits the underlying diagonal or off-diagonal structure of TFD matrices to separate the source signals. In this paper, we propose a new signal-independent kernel which is defined in both the time–lag and the Doppler-lag domain and satisfies most of the desirable properties of a TFD. The main objective of this research is to achieve the high resolution and the maximum cross-term reduction with the preferable diagonal or off-diagonal structure of TFD matrices in BSS applications. Moreover, a BSS approach is developed which includes first whitening mixed signals, then constructing a set of TFD matrices using the proposed TFD and the Hough transform, finally a joint diagonalization of a combined set of TFD matrices to estimate the mixing matrix and the source signals. By use of the techniques proposed in this paper, the improved performance of BSS of nonstationary signals has been achieved.

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...

Monitoring abnormal network traffic based on blind source separation approach

The randomness in network behaviors poses serious challenges for discovering abnormal patterns in network traffic flows. This paper presents a systematic approach for monitoring abnormal network traffic. The DFlow model is proposed to reduce the flow records and extract four features to capture the traffic patterns. The blind source separation method is applied to obtain the routine and abnormal behaviors from those features. A scale space filter is applied to filter the randomness in the traffic flows without affecting the behavior patterns. A threshold is selected based on a systematic criterion to evaluate the degree of abnormality. The contributions of different traffic features to the abnormal behavior detection are analyzed. It is found that the number of connection degree is the most important feature for traffic monitoring. A salient feature of this method is that it is effective for detecting the abnormal behaviors not associated with significant changes in traffic volumes. Another advantage of the new method is that no supervised learning process is needed. This is very important since high quality labeled samples are very difficult to acquire in actual networks especially the data traces associated with attacks. The experimental results based on the actual network data show that the method presented in the paper is effective for monitoring abnormal traffic flows in the gigabytes traffic environment and the accuracy is above 95%.

A Region-Growing Permutation Alignment Approach in Frequency-Domain Blind Source Separation of Speech Mixtures

The convolutive blind source separation (BSS) problem can be solved efficiently in the frequency domain, where instantaneous BSS is performed separately in each frequency bin. However, the permutation ambiguity in each frequency bin should be resolved so that the separated frequency components from the same source are grouped together. To solve the permutation problem, this paper presents a new alignment method based on an inter-frequency dependence measure: the powers of separated signals. Bin-wise permutation alignment is applied first across all frequency bins, using the correlation of separated signal powers; then the full frequency band is partitioned into small regions based on the bin-wise permutation alignment result. Finally, region-wise permutation alignment is performed in a region-growing manner. The region-wise permutation correction scheme minimizes the spreading of the misalignment at isolated frequency bins to others, hence to improve permutation alignment. Experiment results in simulated and real environments verify the effectiveness of the proposed method. Analysis demonstrates that the proposed frequency-domain BSS method is computationally efficient.

Blind Separation and Dereverberation of Speech Mixtures by Joint Optimization

This paper proposes a method for performing blind source separation (BSS) and blind dereverberation (BD) at the same time for speech mixtures. In most previous studies, BSS and BD have been investigated separately. The separation performance of conventional BSS methods deteriorates as the reverberation time increases while many existing BD methods rely on the assumption that there is only one sound source in a room. Therefore, it has been difficult to perform both BSS and BD when the reverberation time is long. The proposed method uses a network, in which dereverberation and separation networks are connected in tandem, to estimate source signals. The parameters for the dereverberation network (prediction matrices) and those for the separation network (separation matrices) are jointly optimized. This enables a BD process to take a BSS process into account. The prediction and separation matrices are alternately optimized with each depending on the other; hence, we call the proposed method the conditional separation and dereverberation (CSD) method. Comprehensive evaluation results are reported, where all the speech materials contained in the complete test set of the TIMIT corpus are used. The CSD method improves the signal-to-interference ratio by an average of about 4 dB over the conventional frequency-domain BSS approach for reverberation times of 0.3 and 0.5 s. The direct-to-reverberation ratio is also improved by about 10 dB.

Extracting Individual Contributions From Their Mixture: A Blind Source Separation Approach

AbstractMultipoint or multichannel observations in plasmas can frequently be modelled as an instantaneous mixture of contributions (waves, emissions, …) of different origins. Recovering the individual sources from their mixture then becomes one of the key objectives. However, unless the underlying mixing processes are well known, these situations lead to heavily underdetermined problems. Blind source separation aims at disentangling such mixtures with the least possible prior information on the sources and their mixing processes. Several powerful approaches have recently been developed, which can often provide new or deeper insight into the underlying physics.This tutorial paper briefly discusses some possible applications of blind source separation to the field of plasma physics, in which this concept is still barely known. Two examples are given. The first shows how concurrent processes in the dynamical response of the electron temperature in a tokamak can be separated. The second example deals with solar spectral imaging in the Extreme UV and shows how empirical temperature maps can be built (© 2011 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Effect of indirect dependencies on maximum likelihood and information theoretic blind source separation for nonlinear mixtures

Two major approaches for blind source separation (BSS) are, respectively, based on the maximum likelihood (ML) principle and mutual information (MI) minimization. They have been mainly studied for simple linear mixtures. We here show that they additionally involve indirect functional dependencies for general nonlinear mixtures. Moreover, the notations commonly employed by the BSS community in calculations performed for these methods may become misleading when using them for nonlinear mixtures, due to the above-mentioned dependencies. In this paper, we first explain this phenomenon for arbitrary nonlinear mixing models. We then accordingly correct two previously published methods for specific nonlinear mixtures, where indirect dependencies were mistakenly ignored. This paper therefore opens the way to the application of the ML and MI BSS methods to many specific mixing models, by providing general tools to address such mixtures and explicitly showing how to apply these tools to practical cases.

Semi-blind source extraction of atrial activity by combining statistical and spectral features

Atrial fibrillation is the most common human arrhythmia. During atrial fibrillation episodes, the surface electrocardiogram contains the linear superposition of the atrial and ventricular rhythms in addition to other non-cardiac artifacts. Since these signals can be considered statistically independent, a Blind Source Separation (BSS) approach fits the problem properly. The signal that contains useful clinical information is the atrial one. We present a solution that focuses on the extraction of the atrial activity, enforcing simultaneously the statistical and temporal properties of the atrial signal. In addition, we propose the use of kurtosis as a parameter to measure the quality of the extraction. The algorithm is applied successfully to synthetic and real data. It improves the extraction of the atrial signal in comparison to other BSS methods, recovers only the interesting atrial rhythm using the information contained in all the leads and reduces the computational cost. The results obtained are shown to be highly satisfactory, with an average of 53.9% of spectral concentration, -0.04 of kurtosis value, 2.98 of ventricular residua and 4.77% of significant QRS residua over a database of thirty patients.

A Comparative Study of Two Blind Source Separation Approaches to Resolve the Multi-Source Limitation of the Nutating Rising-Sun Reticle Based Optical Trackers

A Comparative Study of Two Blind Source Separation Approaches to Resolve the Multi-Source Limitation of the Nutating Rising-Sun Reticle Based Optical Trackers

Rigid Structure from Motion from a Blind Source Separation Perspective

We present an information theoretic approach to define the problem of structure from motion (SfM) as a blind source separation one. Given that for almost all practical joint densities of shape points, the marginal densities are non-Gaussian, we show how higher-order statistics can be used to provide improvements in shape estimates over the methods of factorization via Singular Value Decomposition (SVD), bundle adjustment and Bayesian approaches. Previous techniques have either explicitly or implicitly used only second-order statistics in models of shape or noise. A further advantage of viewing SfM as a blind source problem is that it easily allows for the inclusion of noise and shape models, resulting in Maximum Likelihood (ML) or Maximum a Posteriori (MAP) shape and motion estimates. A key result is that the blind source separation approach has the ability to recover the motion and shape matrices without the need to explicitly know the motion or shape pdf. We demonstrate that it suffices to know whether the pdf is sub-or super-Gaussian (i.e., semi-parametric estimation) and derive a simple formulation to determine this from the data. We provide extensive experimental results on synthetic and real tracked points in order to quantify the improvement obtained from this technique.