Blind Source Separation Problem Research Articles

Tensor decomposition meets blind source separation

In this paper, we investigate the problem of blind source separation (BSS) through the lens of tensor decomposition (TD). Two fundamental connections between TD and BSS are established, forming the basis for two novel tensor-based BSS methods, namely TenSOFO and TCBSS. The former is designed for a joint individual differences in scaling (INDSCAL) decomposition, addressing instantaneous (linear) BSS tasks; while the latter efficiently performs a constrained block term decomposition (BTD), aligning with the design of convolutive BSS. Leveraging the benefits of the alternating direction method of multipliers and the strengths of tensor representations, both TenSOFO and TCBSS prove to be effective in BSS. Our experimental results demonstrate the effectiveness of these two proposed methods in addressing both TD and BSS tasks, particularly when compared to state-of-the-art algorithms.

Modal identification of non‐classically damped structures using generalized sparse component analysis

SummaryModal identification method based on blind source separation (BSS) technique has gained extensive attentions for civil structures. Developing the complex modes estimation method is important in practical applications because the assumption of proportional damping is not always satisfied. Sparse component analysis (SCA) performs well in underdetermined BSS problems. However, SCA is confined to the situation of proportional damping. In this study, a generalized SCA method is proposed to extend the original SCA method to both real and complex modes identification. First, the general formulation of complex modes is extended by the analytic form to eliminate the complex conjugate part in the BSS model. A new single‐source‐point detection method that is available to handle real and complex modes is proposed. Local outlier factor method is adopted to remove the outliers in single source points. Subsequently, complex‐valued modal matrix is calculated by the clustering technique. Then, modal responses are recovered using the complex version of smoothed zero norm method, where modal frequencies and damping ratios can be extracted. Finally, the effectiveness of the proposed method is demonstrated for identification of real and complex modes, close modes, and underdetermined problem. The application to a benchmark structure demonstrates the effectiveness for practical applications.

Rolling bearing compound fault diagnosis based on spatiotemporal intrinsic mode decomposition

Aiming at the vibration signal characteristics of multi-channel rolling bearing complex faults containing various shock components, a rolling bearing complex fault diagnosis model based on spatiotemporal intrinsic mode decomposition (STIMD) method and fast spectral kurtosis method was proposed. The spatiotemporal intrinsic mode decomposition method combines the signal atomic decomposition method with the idea of signal blind source separation. Through the fast independent component analysis and the nonlinear matching pursuit method of the established overcomplete dictionary base, various fault mode components are separated. The initial phase function selected based on the high kurtosis fault frequency band obtained by the fast spectral kurtosis method can better fit the bearing fault frequency domain characteristics, so that the spatiotemporal intrinsic mode decomposition method can more accurately separate various impact components in the vibration signal. The simulation model of bearing compound fault was established and the data collected from fault diagnosis experiment platform were used to verify that the STIMD method was effective in solving the problem of rolling bearing compound fault diagnosis. By analyzing the kurtosis changes under different signal noise ratio (SNR) conditions and comparing the simulation results with the fast independent component analysis method, it shows that the kurtosis index decomposed by the proposed method is more able to prove the existence of faults under the condition of low SNR, that is, the impact is completely covered by noise. Therefore, a spatiotemporal intrinsic mode decomposition method with fast spectral kurtosis optimization can solve the problem of blind source separation in the field of composite faults of multi-channel rolling bearings and realize composite fault diagnosis.

Detection of respiration-induced field modulations in fMRI: A concurrent and navigator-free approach

Abstract Functional Magnetic Resonance Imaging (fMRI) is typically acquired using gradient-echo sequences with a long echo time at high temporal resolution. Gradient-echo sequences inherently encode information about the magnetic field in the often discarded image phase. We demonstrate a method for processing the phase of reconstructed fMRI data to isolate temporal fluctuations in the harmonic fields associated with respiration by solving a blind source separation problem. The fMRI-derived field fluctuations are shown to be in strong agreement with breathing belt data acquired during the same scan. This work presents a concurrent, hardware-free measurement of respiration-induced field fluctuations, providing a respiratory regressor for fMRI analysis which is independent of local contrast changes, and with potential applications in image reconstruction and fMRI analysis.

Dynamic mode decomposition for blindly separating mixed signals and decrypting encrypted images

In this paper, we introduce the dynamic mode decomposition considering a lag $ \tau $ ($ \tau $-DMD) for solving the blind source separation (BSS) problem of chaotic signals and images. $ \tau $-DMD can be used in BSS-based image decryption with good separation performance. The unmixing problem was formulated as a modal decomposition problem. $ \tau $-DMD was applied on separating linear mixed chaotic signals showing a better separation performance than the existing blind source separation algorithms (Amuse, SOBI, FastICA and JADE). In addition, the case of adding noise in the mixing process was considered, and wavelet de-nosing before $ \tau $-DMD improved the separation performance. For the application, $ \tau $-DMD can be used to remove the noise in electrocardiograms (ECG) and the ocular artifacts in electroencephalograms (EEG). $ \tau $-DMD can also be applied in image processing, showing good separation performance of $ \tau $-DMD for both synthetic mixtures and real-life mixed texts. Structural similarity index measurement (SSIM) and peak signal-to-noise ratio (PSNR) were selected as the evaluation criteria. We tested the separation performance of $ \tau $-DMD on natural images, fingerprint images, and real-life text images and compared the results with other methods. Furthermore, $ \tau $-DMD was applied to decrypt the BSS-based encrypted images. In the process of encryption, we set up the underdetermined problem of BSS by mixing the original and key images, and then $ \tau $-DMD was used to extract the original images in the process of decryption with the secret seeds provided. Two simulations were performed to illustrate the performance of $ \tau $-DMD for image decryption, showing a better decryption results than FastICA.

Robust second-order stationary spatial blind source separation using generalized sign matrices

Consider a spatial blind source separation model in which the observed multivariate spatial data are assumed to be a linear mixture of latent stationary spatially uncorrelated random fields. The objective is to recover an unknown mixing procedure as well as the latent random fields. Recently, spatial blind source separation methods that are based on the simultaneous diagonalization of two or more scatter matrices were proposed. In cases involving uncontaminated data, such methods can solve the blind source separation problem, however, in the presence of outlying observations, these methods perform poorly. We propose a robust blind source separation method that employs robust global and local covariance matrices based on generalized spatial signs in simultaneous diagonalization. Simulation studies are employed to illustrate the robustness and efficiency of the proposed methods in various scenarios.

Blind Source Separation with Strength Pareto Evolutionary Algorithm 2 (SPEA2) Using Discrete Wavelet Transform

This paper presents a new method for separating the mixed audio signals of simultaneous speakers using Blind Source Separation (BSS). The separation of mixed signals is an important issue today. In order to obtain more efficient and superior source estimation performance, a new algorithm that solves the BSS problem with Multi-Objective Optimization (MOO) methods was developed in this study. In this direction, we tested the application of two methods. Firstly, the Discrete Wavelet Transform (DWT) was used to eliminate the limited aspects of the traditional methods used in BSS and the small coefficients in the signals. Afterwards, the BSS process was optimized with the multi-purpose Strength Pareto Evolutionary Algorithm 2 (SPEA2). Secondly, the Minkowski distance method was proposed for distance measurement by using density information in the discrimination of individuals with raw fitness values for the concept of Pareto dominance. With this proposed method, the originals (original source signals) were estimated by separating the randomly mixed male and two female speech signals. Simulation and experimental results proved that the efficiency and performance of the proposed method can effectively solve BSS problems. In addition, the Pareto front approximation performance of this method also confirmed that it is superior in the Inverted Generational Distance (IGD) indicator.

CEEMDAN-ICA-Based Radar Monitoring of Adjacent Multi-Target Vital Signs

In recent years, radar, especially frequency-modulated continuous wave (FMCW) radar, has been extensively used in non-contact vital signs (NCVS) research. However, current research does not work when multiple human targets are close to each other, especially when adjacent human targets lie in the same resolution cell. In this paper, a novel method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)–independent component analysis (ICA) was proposed to obtain the vital-sign information (including respiratory rate and heart rate) of adjacent human targets by using a single FMCW radar. Firstly, the data observed at a single angle were decomposed by the CEEMDAN separation algorithm to construct virtual multi-angle observations. It can effectively transform the undetermined blind source separation (UBSS) problem into an overdetermined blind source separation (BSS) problem. Thus, a BSS algorithm based on FastICA can be used to reconstruct each person’s vital-sign signal and then calculate their respiratory rate/heart rate. To validate the effectiveness of the proposed method, experiments based on the measured data were conducted and the results show that the proposed method can obtain multi-target vital-sign information even when they are in the same resolution cell.

Nonlinear independent component analysis for discrete-time and continuous-time signals

We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source’s original component signals) if the mixture is due to a sufficiently differentiable and invertible but otherwise arbitrarily nonlinear function and the component signals of the source are statistically independent with ‘nondegenerate’ second-order statistics. The latter assumption requires the source signal to meet one of three regularity conditions which essentially ensure that the source is sufficiently far away from the nonrecoverable extremes of being deterministic or constant in time. These assumptions, which cover many popular time series models and stochastic processes, allow us to reformulate the initial problem of nonlinear blind source separation as a simple-to-state problem of optimisation-based function approximation. We propose to solve this approximation problem by minimizing a novel type of objective function that efficiently quantifies the mutual statistical dependence between multiple stochastic processes via cumulant-like statistics. This yields a scalable and direct new method for nonlinear Independent Component Analysis with widely applicable theoretical guarantees and for which our experiments indicate good performance.

Scale-certainty geometrically constrained independent vector analysis for determined blind source separation

Output scale ambiguity is a long-standing problem in blind source separation (BSS). Post-process is usually required to rescale the estimated results. Towards avoiding the computation load brought by rescaling post-process, this study proposes a new algorithm called scale-certainty geometrically constrained auxiliary function-based independent vector analysis (SCGC-AuxIVA), which is free of the scale ambiguity problem. SCGC-AuxIVA is derived from GC-AuxIVA by imposing unit response in the target direction as a hard constraint. Experimental results show that SCGC-AuxIVA achieves a comparable separation performance as GC-AuxIVA, while requiring a less computational cost.

Blind separation of noisy piecewise-stationary mixtures via probability measure transform

In this paper, we consider the problem of blind source separation (BSS) under non-Gaussian impulsive noise. We consider the case of overdetermined instantaneous-linear-mixtures of piecewise-stationary signals. These are corrupted by additive stationary noise. Under this framework, we propose a two-stage separation method, called measure-transformed BSS (MT-BSS), that applies a transform to the probability distribution associated with each data segment. The generating function of the transform at hand is a non-negative function, called MT-function, that weights the data points. We show that proper choice of the involved MT-functions can lead to enhanced separation performance. The performance advantage of MT-BSS over alternative BSS techniques is illustrated in simulation examples. In these studies, we consider synthetic data and real audio signals.

Independent vector analysis: Model, applications, challenges

This paper overviews an appealing unsupervised learning method named independent vector analysis (IVA) for its promising applications, such as in audio/speech signal separation, medical signal processing, remote sensing, video/image processing, wireless communication processing, and so on. As a useful data-driven technique in blind source separation (BSS) field, IVA has played an increasingly vital role in dealing with the problems of convolutive mixture separation, multivariate latent variable analysis and multivariate data fusion. IVA extends the conventional independent component analysis (ICA) to multidimensional components, which can result in more available information utilization. Compared with ICA mechanism, IVA is not only to utilize the statistical independence of multivariate signals but also the statistical inner dependency of each multivariate signal. With this generalization, IVA can manipulate some prominent ill-pose issues faced in sensor receiving models and has the advantage to overcome the inherent random permutation ambiguity problem in joint BSS. Motivated by the flexible and versatile technology superiorities of IVA, this paper concentrates on reviewing the IVA model in details, associated methods briefly, and its potential applications as well as prospects. Moreover, some significant open problems about IVA challenges are also discussed in this paper.

A Survey of Optimization Methods for Independent Vector Analysis in Audio Source Separation

With the advent of the era of big data information, artificial intelligence (AI) methods have become extremely promising and attractive. It has become extremely important to extract useful signals by decomposing various mixed signals through blind source separation (BSS). BSS has been proven to have prominent applications in multichannel audio processing. For multichannel speech signals, independent component analysis (ICA) requires a certain statistical independence of source signals and other conditions to allow blind separation. independent vector analysis (IVA) is an extension of ICA for the simultaneous separation of multiple parallel mixed signals. IVA solves the problem of arrangement ambiguity caused by independent component analysis by exploiting the dependencies between source signal components and plays a crucial role in dealing with the problem of convolutional blind signal separation. So far, many researchers have made great contributions to the improvement of this algorithm by adopting different methods to optimize the update rules of the algorithm, accelerate the convergence speed of the algorithm, enhance the separation performance of the algorithm, and adapt to different application scenarios. This meaningful and attractive research work prompted us to conduct a comprehensive survey of this field. This paper briefly reviews the basic principles of the BSS problem, ICA, and IVA and focuses on the existing IVA-based optimization update rule techniques. Additionally, the experimental results show that the AuxIVA-IPA method has the best performance in the deterministic environment, followed by AuxIVA-IP2, and the OverIVA-IP2 has the best performance in the overdetermined environment. The performance of the IVA-NG method is not very optimistic in all environments.

Least-Squares Methods for Nonnegative Matrix Factorization Over Rational Functions

Nonnegative matrix factorization (NMF) models are widely used to analyze linearly mixed nonnegative data. When the data is made of samplings of continuous signals, the factors in NMF can be constrained to be samples of nonnegative rational functions. This leads to a fairly general model referred to as NMF using rational functions (R-NMF). We first show that, unlike NMF, R-NMF possesses an essentially unique factorization under mild assumptions, which is crucial in applications where the ground-truth factors need to be recovered, as in blind source separation problems. Then we present different approaches to solve R-NMF : the R-HANLS, R-ANLS and R-NLS methods. In our tests, no method significantly outperforms the others in all cases, and all three methods offer a different trade-off between solution accuracy and computational requirements. Indeed, while R-HANLS is fast and accurate for large problems, R-ANLS is more accurate, but also more resources demanding, both in time and memory and R-NLS is even more accurate but only for small problems. Then, crucially we show that R-NMF models outperforms NMF in various tasks including the recovery of semi-synthetic continuous signals, and a classification problem of real hyperspectral signals.

Statistically Dependent Blind Signal Separation under Relaxed Sparsity

Most traditional blind source separation (BSS) methods are based on the basic assumption that source signals are mutually independent. However, many signals in the real world are often interrelated to each other. In this paper, a novel BSS method is proposed for dependent signals which only relies on the relaxed sparsity of sources. Under this constraint, the column vector of high-dimensional observed signals would be distributed in a specific subspace. According to the representation relation in time-frequency (TF) domain, each column vector of observed signal is uniquely clustered into the subspace, to which it belongs. Furthermore, the estimation of source signals is calculated by the inverse matrix or the pseudo-inverse matrix of the mixing matrix. It is also demonstrated mathematically and experimentally that under relaxed sparsity conditions, proposed subspace clustering methods is promising and hopeful to solve the dependent BSS (DBSS) problems.

Unique estimation in EEG analysis by the ordering ICA.

Independent Component Analysis (ICA) is a method for solving blind source separation problems. Because ICA only needs weak assumptions to estimate the unknown sources from only the observed signals, it is suitable for Electroencephalography (EEG) analysis. A serious disadvantage of the traditional ICA algorithms is that their results often fluctuate and do not converge to the unique and globally optimal solution at each run. It is because there are many local optima and permutation ambiguities. We have recently proposed a new ICA algorithm named the ordering ICA, a simple extension of Fast ICA. The ordering ICA is theoretically guaranteed to extract the independent components in the unique order and avoids the local optima in practice. This paper investigated the usefulness of the ordering ICA in EEG analysis. Experiments showed that the ordering ICA could give unique solutions for the signals with large non-Gaussianity, and the ease of parallelization could reduce computation time.

Acoustic UAV detection method based on blind source separation framework

Many new challenges are encountered in public security because of the rapid development of an unmanned aerial vehicle (UAV) technology. In order to meet these challenges brought by UAV, it is necessary to realize timely and accurate UAV detection. In this paper, an acoustic UAV detection method based on blind source separation (BSS) framework is introduced to solve the UAV sound detection problem with multi-source interference. In the framework proposed in this paper, source number estimation is used to determine the type of BSS problem, and three methods are applied to separate the UAV sound from the mixing signal in different BSS situations. In the experiment, a variety of machine learning algorithms are used to detect UAVs. The robustness of the proposed method is tested on different UAVs and different sound features. Experimental results show that the UAV sound detection method based on the BSS framework realizes the effective detection of UAVs in different tests and achieves excellent robustness. Compared with mixed signal and filtered signal, the detection rate of our scheme is more than 90%, whether in the overdetermined, positive-definite, and underdetermined cases.

Functional Split of In-Network Deep Learning for 6G: A Feasibility Study

In existing mobile network systems, the data plane (DP) is mainly considered a pipeline consisting of network elements end-to-end forwarding user data traffics. With the rapid maturity of programmable network devices, however, mobile network infrastructure mutates towards a programmable computing platform. Therefore, such a programmable DP can provide in-network computing capability for many application services. In this paper, we target to enhance the data plane with in-network deep learning (DL) capability. However, in-network intelligence can be a significant load for network devices. Then, the paradigm of the functional split is applied so that the deep neural network (DNN) is decomposed into sub-elements of the data plane for making machine learning inference jobs more efficient. As a proof-of-concept, we take a Blind Source Separation (BSS) problem as an example to exhibit the benefits of such an approach. We implement the proposed enhancement in a full-stack emulator and we provide a quantitative evaluation with professional datasets. As an initial trial, our study provides insightful guidelines for the design of the future mobile network system, employing in-network intelligence (e.g., 6G).

Semi-Blind Source Separation with Learned Constraints

Blind source separation (BSS) algorithms are unsupervised methods, which are the cornerstone of hyperspectral data analysis by allowing for physically meaningful data decompositions. BSS problems being ill-posed, the resolution requires efficient regularization schemes to better distinguish between the sources and yield interpretable solutions. For that purpose, we investigate a semi-supervised source separation approach in which we combine a projected alternating least-square algorithm with a learning-based regularization scheme. In this article, we focus on constraining the mixing matrix to belong to a learned manifold by making use of generative models. Altogether, we show that this allows for an innovative BSS algorithm, with improved accuracy, which provides physically interpretable solutions. The proposed method, coined sGMCA, is tested on realistic hyperspectral astrophysical data in challenging scenarios involving strong noise, highly correlated spectra and unbalanced sources. The results highlight the significant benefit of the learned prior to reduce the leakages between the sources, which allows an overall better disentanglement.

A New Robust Adaptive Algorithm for Second Order Blind Source Separation

This paper deals with the adaptive blind source separation problem in presence of impulsive noise. New algorithms extending the well known SOBI method from batch to adaptive scheme are introduced. At first, the standard Gaussian noise case is considered, leading to our first algorithm referred to as Adaptive SOBI (A-SOBI). Later on, a robust version of A-SOBI, referred to as RA-SOBI is derived to handle the impulsive noise case. RA-SOBI relies on robust subspace tracking for the whitening stage together with robust correlation estimation for the separation stage. All proposed algorithms are of relatively low complexity and allow to achieve good separation quality as illustrated by our simulation results.