Chapter 1 - Introduction

The most standard blind source separation (BSS) methods address the situation when a set of signals are available, e.g. from measurements, and all of them are linear memoryless combinations, with unknown coefficient values, of the same limited set of unknown source signals. BSS methods aim at estimating these unknown source signals and/or coefficients. This generic problem is e.g. faced in the field of Earth observation (where it is also called “unsupervised unmixing”), when considering the commonly used (over)simplified model of hyperspectral images. Each pixel of such an image has an associated reflectance spectrum derived from measurements, which is defined by the fraction of sunlight power reflected by the corresponding Earth surface at each wavelength. Each source signal is then the single reflectance spectrum associated with one of the classes of pure materials which are present in the region of Earth corresponding to the overall considered hyperspectral image. Besides, the associated coefficients define the surfaces on Earth covered with each of these pure materials in each sub-region corresponding to one pixel of the considered image. However, real hyperspectral data e.g. obtained in urban areas have a much more complex structure than the above basic model: each class of pure materials (e.g. roof tiles, trees or asphalt) has so-called spectral or intra-class variability, i.e. it yields a somewhat different spectral component in each pixel of the image. In this complex framework, this chapter shows that Principal Component Analysis (PCA) and its proposed extension are of high interest at three stages of our investigation. First, PCA allows us to analyze the above-mentioned spectral variability of real high-dimensional hyperspectral data and to propose an extended data model which is suited to these complex data. We then develop a versatile extension of BSS methods based on Nonnegative Matrix Factorization, which adds the capability to handle arbitrary forms of intra-class variability by transposing PCA concepts to this original version of the BSS tramework. Finally, PCA again proves to be very well suited to analyzing the high-dimensional data obtained as the result of the proposed BSS method.

In the recent past, blind source separation (BSS) algorithms using multivariate statistical data analysis technique have been successfully used for source identification and separation in the field of biomedical and statistical signal processing. Recently numbers of different BSS techniques have been developed. With BSS methods being the feasible method for source separation and decomposition of biosignals, it is important to compare the different techniques and determine the most suitable method for the applications. This paper presents the performance of five BSS algorithms (SOBI, TDSEP, FastICA, JADE and Infomax) for decomposition of sEMG to identify subtle finger movements. It is observed that BSS algorithms based on second-order statistics (SOBI and TDSEP) gives better performance compared to algorithms based on higher-order statistics (FastICA, JADE and infomax).

This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method.

Upgrading Sparse NMF algorithm for blind source separation through Adaptive Parameterized Hybrid Kernel based approach

Blind source separation and feature extraction in concurrent control charts pattern recognition: Novel analyses and a comparison of different methods

The methods that can be done for the estimation of the number of source signals and separation of source signals using time‐frequency information are proposed as a method of blind source separation. In these methods, some independent conditions are assumed in a time‐frequency domain, and observed signals are expanded to time‐frequency domain using wavelet analysis. However, these methods are not considered phase differences (difference of distance) between source signals and observed signals. A new method is proposed. The method can be done not only for the source separation but also the specification of the locations of source signals considering phase differences. In this method, it is necessary to assume a rather stronger independent condition than former methods. But, on account of this assumption, a function that becomes a real value only when phase differences are coincidence in time‐frequency domain is determined. Using this function, first of all, the number of source signals is calculated, then the locations of source signals and source signals are calculated. The effectiveness of the method is shown using actual synthetic signals.

For the problem of blind source separation (BSS) with the sparsity properties of the high frequency wavelet transform coefficients, the paper proposed a new method based on compressed sensing (CS) and K-means clustering algorithm. Compared with the traditional methods of blind source separation, simulation results demonstrated that the proposed method improves the quality of the recovered signal significantly, and improves the speed of separating and reconstruction obviously.

Recently, blind source separation (BSS) methods have gained significant attention in the area of signal processing. Independent component analysis (ICA) and second-order blind identification (SOBI) are two popular BSS methods that have been applied to modal identification of mechanical and structural systems. Published results by several researchers have shown that ICA performs satisfactorily for systems with very low levels of structural damping, for example, for damping ratios of the order of 1% critical. For practical structural applications with higher levels of damping, methods based on SOBI have shown significant improvement over ICA methods. However, traditional SOBI methods suffer when nonstationary sources are present, such as those that occur during earthquakes and other transient excitations. In this paper, a new technique based on SOBI, called the modified cross-correlation method, is proposed to address these shortcomings. The conditions in which the problem of structural system identification can be posed as a BSS problem is also discussed. The results of simulation described in terms of identified natural frequencies, mode shapes, and damping ratios are presented for the cases of synthetic wind and recorded earthquake excitations. The results of identification show that the proposed method achieves better performance over traditional ICA and SOBI methods. Both experimental and large-scale structural simulation results are included to demonstrate the applicability of the newly proposed method to structural identification problems.

In recent years, much research has been focused on separating acoustic sources from their mixtures. Degenerate Unmixing Estimation Technique (DUET) is one of the widely popular methods of Blind Source Separation (BSS) in underdetermined scenarios. DUET is based on a signal recovery sparsity algorithm whose performance is strongly influenced by sparsity in the Time-Frequency (TF) domain. Noises and an several sources in mixtures limit the sparsity resulting in performance degradation in DUET. Here an enhanced strategy has been adopted by combining DUET with adaptive noise cancellation utilising the Dual-Tree Complex Wavelet Transform (DTCWT) as a pre-processor and TF refinement utilising Synchroextracting Transform (SET) as a post-processor. This improves the sparsity of sources and energy concentrations in a TF representation. Results of the signal separation performance evaluation reveal that the proposed algorithm outperforms conventional DUET in signal separation, especially in real-time scenarios.

Event-related potentials (ERPs) are a superposition of electric potential differences generated by neurophysiological activity associated with psychophysical events. Spatiotemporal dissociation of these signal sources can supplement conventional ERP analysis and improve source localization. However, results from established source separation methods applied to ERPs can be challenging to interpret. Hence, we have developed a recurrent neural network (RNN) method for blind source separation. The RNN transforms input step pulse signals representing events into corresponding ERP difference waveforms. Source waveforms are obtained from penultimate layer units and scalp maps are obtained from feed-forward output layer weights that project these source waveforms onto EEG electrode amplitudes. An interpretable, sparse source representation is achieved by incorporating L1 regularization of signals obtained from the penultimate layer of the network during training. This RNN method was applied to four ERP difference waveforms (MMN, N170, N400, P3) from the open-access ERP CORE database, and independent component analysis (ICA) was applied to the same data for comparison. The RNN decomposed these ERPs into eleven spatially and temporally separate sources that were less noisy, tended to be more ERP-specific, and were less similar to each other than ICA-derived sources. The RNN sources also had less ambiguity between source waveform amplitude, scalp potential polarity, and equivalent current dipole orientation than ICA sources. In conclusion, the proposed RNN blind source separation method can be effectively applied to grand-average ERP difference waves and holds promise for further development as a computational model of event-related neural signals.

Conventionally, there is a method to use auscultation when medical doctors diagnose a disease from heartbeats with heart noise. However, the respiratory sound and the heart sound are mixed. Further, it is difficult for the desired heart sound to be heard. For solving this problem, we propose a method to separate respiratory sound and heart sound based on blind source separation (BSS). In BSS method, we use a non-linear function corresponding to the probability distribution of source signals in order to separate. A distribution of the respiratory sound is a high-order sub-Gaussian distribution close to uniform distribution, a distribution of the heart sound is a super Gaussian distribution. In the conventional method, there is no non-linear function corresponding to both distribution. Therefore, in this paper, in order to separate the respiratory sound and the heart sound, we propose new non-linear function accurately separated from super Gaussian distribution through sub-Gaussian distribution to uniform distribution. Then, we build the BSS method based on the proposed non-linear function. We evaluate the proposed method by computer simulation.

The problem of blind source separation (BSS) for multiple-input multiple-output (MIMO) autoregressive (AR) mixtures is addressed in this paper. A new time-domain method for system identification and BSS is proposed based on the Gaussian mixture model (GMM) for sources distribution. The algorithm is based on the generalized expectation-maximization (GEM) method for joint estimation of the AR model parameters and the GMM parameters of the sources. The method is tested via simulations of synthetic and real audio signals. The results show that the proposed algorithm outperforms the well-known multidimensional linear predictive coding (LPC), and it achieves higher signal-to-interference ratio (SIR) in the BSS problem.

A novel semi-blind source separation framework towards maximum signal-to-interference ratio

This paper addresses the determined convolutive blind source separation (BSS) problem. The state-of-the-art independent low-rank matrix analysis (ILRMA), unifying independent component analysis (ICA) and nonnegative matrix factorization, has the disadvantage of ignoring inter-frame and inter-frequency spectral correlation of source signals. We here propose a new BSS method that estimates a linear transformation for spectral decorrelation and performs ILRMA in the transformed domain. A newly introduced optimization problem is an extension of that for ICA based on maximum likelihood. For this problem, we provide a necessary and sufficient condition for the existence of optimal solutions, and develop algorithms based on block coordinate descent methods with closed-form solutions. Experimental results show the improved separation performance of the proposed method compared to ILRMA.

A new method for solving the permutation problem in the frequency-domain Blind Source Separation(BSS) was presented.This new method divided the whole frequency-domain into three sections and applied different permutation algorithms to different sections.The neighboring frequency correlation and harmonic frequency correlation coefficient of signal amplitudes were used together for the low-frequency section,the direction of arrival estimation for speech sources for the mid-frequency section,and the combination of correlation coefficient comparison and direction estimation for the high-frequency section,respectively.Experimental results show that the new method provides a more robust and precise solution to the permutation problem than the algorithm only with interfrequency correlation coefficient of signal amplitudes or only with direction of arrival estimation for sources.