Cooperative Wiener-ICA for source localization and Separation by distributed microphone arrays

This keynote talk describes a state-of-the-art method for the blind source separation (BSS) of convolutive mixtures of audio signals. Independent component analysis (ICA) is used as a major statistical tool for separating the mixtures. We provide examples to show how ICA criteria change as the number of audio sources increases. We then discuss a frequency-domain approach where simple instantaneous ICA is employed in each frequency bin. A directivity pattern analysis of the ICA solutions provides us with a physical interpretation of the ICA-based separation. It tells us the relationship between ICA-based BSS and adaptive beamforming. In order to obtain properly separated signals with the frequency-domain approach, the permutation and scaling ambiguity of the ICA solutions should be aligned appropriately. We describe two complementary methods for aligning the permutations, i.e., collecting separated frequency components originating from the same source. The first method exploits the signal envelope dependence of the same source across frequencies. The second method relies on the spatial diversity of the sources, and is closely related to source localization techniques. Finally, we describe methods for sparse source separation, which can be applied even to an underdetermined case.

Editorial Source separation is not a new problem. We, human beings, as well as many other species, do it unconsciously at every instant of our lives. Our organisms receive a multitude of signals mixed together from the environment, and we are constantly uncovering the relevant ones in order to derive vital information to continue our lives. Other than the biological signals that are occurring at the cell or organ level, there are also various source separation tasks that we consciously do daily. In a crowded underground, room or office, we try to extract what our friend or colleague is telling us among all other speech or audial signals arriving at our ears. Although the source separation problem is handled rather seamlessly by our brains, its implementation in computers has required the development of mathematical models and algorithms. Starting in the 1980s, the problem has been addressed firstly in the context of the cocktail party problem: how to separate a number of speech signals from multichannel mixtures of them. Originally, a simple model of linear mixing was adopted. A solution has been provided to this simplified problem by the independent component analysis algorithm. Later, several other applications have been considered with source separation problems ranging from financial time series analysis to functional magnetic resonance imaging, and from cosmological image separation to music signal separation. The model has been extended to convolutive mixtures and to non-linear mixtures, and variations of the independent component analysis (ICA) algorithm have been utilised. The essence behind independent component analysis is the assumption of statistical independence of the sources. Since the problem is a blind one, that is, we do not know the channel (mixing) characteristics, the mixture model alone represents an ill-posed problem, and we need additional information to resolve the unmixing. The independence assumption provides this additional

We present a new approach to independent component analysis (ICA) by extending the formulation of univariate source signals to multivariate source signals. The new approach is termed independent vector analysis (IVA). In the model, we assume that linear mixing model exists in each dimension separately, and the latent sources are independent of the others. In contrast to ICA, the sources are random vectors, not just single variables, which means the elements of a random vector are closely related to the others. Thus, we assume the dependency between the elements of a source vector. In this manner, we define dependence between vectors as Kullback-Leibler divergence between the total joint probability of vectors and the product of marginal probabilities of vectors. Then, the model allows independence between multivariate source signals represented as random vectors, and dependence between the source signals within the vector representation. The proposed vector density model can for example capture variance dependencies within a vector source signal. There are several applications of this new formulation. In the separation of acoustic sources, the algorithm mitigates the permutation problem, i.e. the usual ICA algorithms applied in to the frequency domain mixture data suffer from the unknown permutation of the output signals. Although there are several engineering solutions to fix this problem after the ICA stage, the proposed method provides a natural solution to the problem by capturing the inherent dependencies of the acoustic signals. It therefore avoids the permutation problem and allows the separation of sources in very challenging environments for many sound sources.

Blind Signal Separation II. Linear, Convolutive Combinations: II. Linear, Convolutive Combinations

The problem of blind source separation (BSS) has been intensively studied by the signal processing community. The first solutions to deal with BSS were proposed in the 1980's and are founded on the concept of independent component analysis (ICA). More recently, aiming at tackling some limitations of ICA-based methods, much attention has been paid to alternative BSS approaches. In this tutorial, in addition to providing a brief review of the classical BSS framework, we present two research trends in this area, namely source separation over Galois fields and sparse component analysis. For both subjects, we provide an overview of the main criteria, highlighting scenarios that can benefit from these more recent BSS paradigms.

We propose a new algorithm for blind source separation (BSS), in which independent component analysis (ICA) and beamforming are combined to resolve the low-convergence problem through optimization in ICA. The proposed method consists of the following three parts: (1) frequency-domain ICA with direction-of-arrival (DOA) estimation, (2) null beamforming based on the estimated DOA, and (3) integration of (1) and (2) based on the algorithm diversity in both iteration and frequency domain. The inverse of the mixing matrix obtained by ICA is temporally substituted by the matrix based on null beamforming through iterative optimization, and the temporal alternation between ICA and beamforming can realize fast- and high-convergence optimization. The results of the signal separation experiments reveal that the signal separation performance of the proposed algorithm is superior to that of the conventional ICA-based BSS method, even under reverberant conditions.

The independent component analysis and wavelet transform technology are used to separate and identify the internal combustion engine noise signal. According to the basic principle of independent component analysis, FastICA based on negative entropy great with the good stability and convergence speed algorithm is applied to separate the noise signals of six cylinder diesel engine. And the noise signals are decomposed into a series of independent components. The fast Fourier transform and wavelet transform technology are applied on each independent component analysis. Combining with the time-frequency analysis results and the internal combustion engine noise signal spectrum and the structure of the separation of the independent component and getting the corresponding relationship of different internal combustion engine noise sources. The results show that: the independent components correspond to the diesel engine combustion noise sources, the piston knock noise, and fuel injection pump noise and so on.

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.

Source-space ICA for EEG source separation, localization, and time-course reconstruction

We propose a new algorithm for blind source separation (BSS), in which independent component analysis (ICA) and beamforming are combined to resolve the low-convergence problem through optimization in ICA. The proposed method consists of the following three parts: (1) frequency-domain ICA with direction-of-arrival (DOA) estimation; (2) null beamforming based on the estimated DOA; (3) integration of (1) and (2) based on the algorithm diversity in both iteration and frequency domain. The inverse of the mixing matrix obtained by ICA is temporally substituted by the matrix based on null beamforming through iterative optimization, and the temporal alternation between ICA and beamforming can realize fast- and high-convergence optimization. The results of the signal separation experiments reveal that the signal separation performance of the proposed algorithm is superior to that of the conventional ICA-based BSS method, even under reverberant conditions.

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.

We propose methods to analyze and control source localization of stereo audio signals using blind source separation (BSS) based on independent component analysis (ICA). Although an inverse system of separation compensates distortion caused by ICA as reconstruction of stereo spatial characteristics, this technique is insufficient to analyze localization because it achieves compensation of distortion and reconstruction of spatial characteristics simultaneously. Thus we analyze spatial characteristics effectively by dividing the compensation into two steps: monaural-output compensation of distortion and its reconstruction of spatial characteristics. Additionally, we control the localization of each source by modifying the analyzed spatial characteristics. It is shown that the proposed method can be applied to stereo signals consisting of more than two sources.

Blind source separation (BSS) aims at separating useful signal content from distortions. In the contactless acquisition of vital signs by means of the camera-based photoplethysmogram (cbPPG), BSS has evolved the most widely used approach to extract the cardiac pulse. Despite its frequent application, there is no consensus about the optimal usage of BSS and its general benefit. This contribution investigates the performance of BSS to enhance the cardiac pulse from cbPPGs in dependency to varying input data characteristics. The BSS input conditions are controlled by an automated spatial preselection routine of regions of interest. Input data of different characteristics (wavelength, dominant frequency, and signal quality) from 18 postoperative cardiovascular patients are processed with standard BSS techniques, namely principal component analysis (PCA) and independent component analysis (ICA). The effect of BSS is assessed by the spectral signal-to-noise ratio (SNR) of the cardiac pulse. The preselection of cbPPGs, appears beneficial providing higher SNR compared to standard cbPPGs. Both, PCA and ICA yielded better outcomes by using monochrome inputs (green wavelength) instead of inputs of different wavelengths. PCA outperforms ICA for more homogeneous input signals. Moreover, for high input SNR, the application of ICA using standard contrast is likely to decrease the SNR.

Advances in machine learning (ML) and the internet-of-things (IoT) have resulted in a renewed interest in analog matrix-vector multiplication (MvM) accelerators [1–3]. Classification based tasks have exploited low-to-medium resolution multiplication and accuracy boosting algorithms in order to compensate for the reduced resolution. Complementing classification, tasks like source separation and localization have diverse applications ranging from signal conditioning in communication [4] and ultrasound to electroencephalography (EEG) [5] source localization and spike sorting, and greatly benefit from similar algorithms. However, due to their lower resolution and limited channel count previously developed systems cannot be directly applied to this task. High-resolution analog multiplication introduces challenges that have limited prior work to less than 6-bit multiplication in the analog domain. Alternative approaches utilizing very high oversampling result in very inefficient solutions. High precision in matrix-multiplication can mitigate the effects of ill-conditioned (almost singular) matrices, as with beamforming separation of near-collinear sources, and other tasks incurring principal component analysis [3] or independent component analysis (ICA) [5]. As seen in Fig. 21.7.1, a large signal dynamic range at the input can results in an untenable dynamic range specification on the downstream data-converters leading to greater than 10× increase in power [4]. Thus, we present a multichannel multiple-input multiple-out (MIMO) mixed-signal linear transform system, with analog signal path and digital coefficient control, composed of an array of 14-bit Nested Thermometer Multiplying DACs (NTMDACs) implementing analog multiplication, and variable gain amplifier (VGA) implementing accumulation. We demonstrate state-of-the art performance on two tasks, spectrally oblivious interference suppression in communication signals and EEG signal separation.

Independent Component Analysis (ICA) is based on the linear mixture model of hyperspectral data and has been widely used in various blind source separations. Non-negative ICA considers non negativity constraint in addition to independency of components and the results will therefore be more real because negative signal sources in an image are not physically meaningful. The non-negative Independent Component Analysis (ICA) was used for detection and mapping of endmembers on a Hyperspectral dataset in this study. This paper surveys the capability of non-negative ICA for endmember detection and unmixing of Hyperion data in a geological terrain. In this research, a small part of the Hyperion scene was processed using the geodesic search algorithm to distinguish the Independent Components (ICs) of the image. The dataset was first topographically and atmospherically corrected and then data quality assessment was performed for recognizing the bad bands. The applied method for unmixing was able to detect the major minerals in the study scene and resulted in more accurate outcome in comparison to regular ICA. The non-negative ICA algorithm satisfactory identified three ICs, of which one showed considerable abundances in the region. The determined minerals are also more compatible to the geology and lithological features in the region. It therefore can map alterations and minerals abundances with higher accuracy. The abundances map of detected minerals was generated using spectral angle mapper method that proved as a useful tool for this purpose.