Second-order Blind Source Separation Research Articles

Atrial Periodic Source Spectrum from Preoperative Body Surface Potentials Predicts Long-term Recurrence of Atrial Fibrillation.

About half of patients experience recurrence of atrial fibrillation (AF) within three to five years after a single catheter ablation procedure. The suboptimality of the long-term outcomes likely results from the inter-patient variability of AF mechanisms, which can be remedied by improved patient screening. We aim to improve the interpretation of body surface potentials (BSPs), such as 12-lead electrocardiograms and 252-lead BSP maps, to aid preoperative patient screening. We developed the Atrial Periodic Source Spectrum (APSS), a novel patient-specific representation based on atrial periodic content, computed on the f-wave segments of patient BSPs, using a second-order blind source separation and a Gaussian Process for regression. With follow-up data, Cox's proportional hazard model was used to select the most relevant feature from preoperative APSSs responsible for AF recurrence. Over 138 persistent AF patients, the presence of highly periodic content with cycle lengths between 220-230 ms or 350-400 ms indicates higher risks of 4-year post-ablation AF recurrence (log-rank test, p-value ). Preoperative BSPs demonstrate effective prediction in the long-term outcomes, highlighting their potential for patient screening in AF ablation therapy.

Detection of focal source and arrhythmogenic substrate from body surface potentials to guide atrial fibrillation ablation.

Focal sources (FS) are believed to be important triggers and a perpetuation mechanism for paroxysmal atrial fibrillation (AF). Detecting FS and determining AF sustainability in atrial tissue can help guide ablation targeting. We hypothesized that sustained rotors during FS-driven episodes indicate an arrhythmogenic substrate for sustained AF, and that non-invasive electrical recordings, like electrocardiograms (ECGs) or body surface potential maps (BSPMs), could be used to detect FS and AF sustainability. Computer simulations were performed on five bi-atrial geometries. FS were induced by pacing at cycle lengths of 120–270 ms from 32 atrial sites and four pulmonary veins. Self-sustained reentrant activities were also initiated around the same 32 atrial sites with inexcitable cores of radii of 0, 0.5 and 1 cm. FS fired for two seconds and then AF inducibility was tested by whether activation was sustained for another second. ECGs and BSPMs were simulated. Equivalent atrial sources were extracted using second-order blind source separation, and their cycle length, periodicity and contribution, were used as features for random forest classifiers. Longer rotor duration during FS-driven episodes indicates higher AF inducibility (area under ROC curve = 0.83). Our method had accuracy of 90.6±1.0% and 90.6±0.6% in detecting FS presence, and 93.1±0.6% and 94.2±1.2% in identifying AF sustainability, and 80.0±6.6% and 61.0±5.2% in determining the atrium of the focal site, from BSPMs and ECGs of five atria. The detection of FS presence and AF sustainability were insensitive to vest placement (±9.6%). On pre-operative BSPMs of 52 paroxysmal AF patients, patients classified with initiator-type FS on a single atrium resulted in improved two-to-three-year AF-free likelihoods (p-value < 0.01, logrank tests). Detection of FS and arrhythmogenic substrate can be performed from ECGs and BSPMs, enabling non-invasive mapping towards mechanism-targeted AF treatment, and malignant ectopic beat detection with likely AF progression.

The Masking Impact of Intra-Artifacts in EEG on Deep Learning-Based Sleep Staging Systems: A Comparative Study.

Elimination of intra-artifacts in EEG has been overlooked in most of the existing sleep staging systems, especially in deep learning-based approaches. Whether intra-artifacts, originated from the eye movement, chin muscle firing, or heart beating, etc., in EEG signals would lead to a positive or a negative masking effect on deep learning-based sleep staging systems was investigated in this paper. We systematically analyzed several traditional pre-processing methods involving fast Independent Component Analysis (FastICA), Information Maximization (Infomax), and Second-order Blind Source Separation (SOBI). On top of these methods, a SOBI-WT method based on the joint use of the SOBI and Wavelet Transform (WT) is proposed. It offered an effective solution for suppressing artifact components while retaining residual informative data. To provide a comprehensive comparative analysis, these pre-processing methods were applied to eliminate the intra-artifacts and the processed signals were fed to two ready-to-use deep learning models, namely two-step hierarchical neural network (THNN) and SimpleSleepNet for automatic sleep staging. The evaluation was performed on two widely used public datasets, Montreal Archive of Sleep Studies (MASS) and Sleep-EDF Expanded, and a clinical dataset that was collected in Huashan Hospital of Fudan University, Shanghai, China (HSFU). The proposed SOBI-WT method increased the accuracy from 79.0% to 81.3% on MASS, 83.3% to 85.7% on Sleep-EDF Expanded, and 75.5% to 77.1% on HSFU compared with the raw EEG signal, respectively. Experimental results demonstrate that the intra-artifacts bring out a masking negative impact on the deep learning-based sleep staging systems and the proposed SOBI-WT method has the best performance in diminishing this negative impact compared with other artifact elimination methods.

A new method for blind identification of structures with limited sensors

In this paper, a new identification method based on second-order blind source separation (SOBSS) has been proposed. A major restriction of the standard SOBSS algorithm in the identification context is that the responses in all degree of freedoms (DOFs) should be recorded. Several studies have already been carried out to overcome this issue by synthetically increasing the number of responses. Using a different strategy, in this paper, the problem has been resolved by reducing the number of active modes in the measurements using the filtering technique. The measurements are filtered according to their Fourier spectra such that the number of active modes in the filtered responses is equal to the number of sensors. Then, the SOBSS algorithm is applied to the filtered responses to obtain the modal coordinates and mode shape vectors. Two numerical simulations and a finite element model of a benchmark structure have been used to evaluate the accuracy of the proposed method. The results show that the proposed method can accurately extract the modal parameters of the structures using limited sensors, in both the cases of free or ambient vibrations. However, in the case of poorly excited modes, greater accuracy can be achieved by increasing the number of measured DOFs. Owing to the filtering step, the proposed method showed a much better performance in the case of noisy measurements, in comparison with the standard SOBSS algorithm.

Separation and identification of structural modes in largely underdetermined scenarios using frequency banding

In recent years, blind source separation (BSS) has gained significant interest in the context of operational modal analysis, as a non-parametric alternative to the identification of mechanical structures from output-only measurements. One persisting limitation of most BSS methods, however, is to they cannot identify more active modes than the number of simultaneously measured outputs. The aim of this work is to propose a solution to the largely underdetermined case – where many more modes are to be identified than the number of available measurements -- by dividing the frequency axis in subbands, such that each band provides an (over)determined problem where BSS can be applied separately. The approach comes with the proposal of a new second-order BSS that operates directly in the frequency domain and takes as an input the cross-spectral matrix of the data. A data augmentation technique is also devised to artificially increase the dimension of the measurements in severely undetermined scenarios. Finally, an identification algorithm is introduced that estimates the modal parameters of the separated structural modes. A remarkable aspect of these algorithms is that they are all based on the unified use of multi-filters designed in the frequency domain, yet with different frequency bandwidths. Another particularity of the present paper is to demonstrate the validity of the proposed approach on several benchmark databases with various degrees of difficulty including complex modes, high modal overlap, singular modes, and the presence of engine harmonics. In all cases, the proposed methodology was efficient and, above all, easy to deal with even in largely undetermined cases.

A second-order blind source separation method for bilinear mixtures

In this paper, we are interested in the problem of Blind Source Separation using a Second-order Statistics (SOS) method in order to separate autocorrelated and mutually independent sources mixed according to a bilinear (BL) model. In this context, we propose a new approach called Bilinear Second-order Blind Source Separation, which is an extension of linear SOS methods, devoted to separate sources present in BL mixtures. These sources, called extended sources, include the actual sources and their products. We first study the statistical properties of the different extended sources, in order to verify the assumption of identifiability when the actual sources are zero-mean and when they are not. Then, we present the different steps performed in order to estimate these actual centred sources and to extract the actual mixing parameters. The obtained results using artificial mixtures of synthetic and real sources confirm the effectiveness of the new proposed approach.

Denoising of HD-sEMG signals using canonical correlation analysis.

High-density surface electromyography (HD-sEMG) is a recent technique that overcomes the limitations of monopolar and bipolar sEMG recordings and enables the collection of physiological and topographical informations concerning muscle activation. However, HD-sEMG channels are usually contaminated by noise in an heterogeneous manner. The sources of noise are mainly power line interference (PLI), white Gaussian noise (WGN) and motion artifacts (MA). The spectral components of these disruptive signals overlap with the sEMG spectrum which makes classical filtering techniques non effective, especially during low contraction level recordings. In this study, we propose to denoise HD-sEMG recordings at 20% of the maximum voluntary contraction by using a second-order blind source separation technique, named canonical component analysis (CCA). For this purpose, a specific and automatic canonical component selection, using noise ratio thresholding, and a channel selection procedure for the selective version (sCCA) are proposed. Results obtained from the application of the proposed methods (CCA and sCCA) on realistic simulated data demonstrated the ability of the proposed approach to retrieve the original HD-sEMG signals, by suppressing the PLI and WGN components, with high accuracy (for five different simulated noise dispersions using the same anatomy). Afterward, the proposed algorithms are employed to denoise experimental HD-sEMG signals from five healthy subjects during biceps brachii contractions following an isometric protocol. Obtained results showed that PLI and WGN components could be successfully removed, which enhances considerably the SNR of the channels with low SNR and thereby increases the mean SNR value among the grid. Moreover, the MA component is often isolated on specific estimated sources but requires additional signal processing for a total removal. In addition, comparative study with independent component analysis, CCA-wavelet and CCA-empirical mode decomposition (EMD) proved a higher efficiency of the presented method over existing denoising techniques and demonstrated pointless a second filtering stage for denoising HD-sEMG recordings at this contraction level.

A Penalized Semialgebraic Deflation ICA Algorithm for the Efficient Extraction of Interictal Epileptic Signals.

As a noninvasive technique, electroencephalography (EEG) is commonly used to monitor the brain signals of patients with epilepsy such as the interictal epileptic spikes. However, the recorded data are often corrupted by artifacts originating, for example, from muscle activities, which may have much higher amplitudes than the interictal epileptic signals of interest. To remove these artifacts, a number of independent component analysis (ICA) techniques were successfully applied. In this paper, we propose a new deflation ICA algorithm, called penalized semialgebraic unitary deflation (P-SAUD) algorithm, that improves upon classical ICA methods by leading to a considerably reduced computational complexity at equivalent performance. This is achieved by employing a penalized semialgebraic extraction scheme, which permits us to identify the epileptic components of interest (interictal spikes) first and obviates the need of extracting subsequent components. The proposed method is evaluated on physiologically plausible simulated EEG data and actual measurements of three patients. The results are compared to those of several popular ICA algorithms as well as second-order blind source separation methods, demonstrating that P-SAUD extracts the epileptic spikes with the same accuracy as the best ICA methods, but reduces the computational complexity by a factor of 10 for 32-channel recordings. This superior computational efficiency is of particular interest considering the increasing use of high-resolution EEG recordings, whose analysis requires algorithms with low computational cost.

A Modal Identification Algorithm Combining Blind Source Separation and State Space Realization

A modal identification algorithm is developed, combining techniques from Second Order Blind Source Separation (SOBSS) and State Space Realization (SSR) theory. In this hybrid algorithm, a set of correlation matrices is generated using time-shifted, analytic data and assembled into several Hankel matrices. Dissimilar left and right matrices are found, which diagonalize the set of nonhermetian Hankel matrices. The complex-valued modal matrix is obtained from this decomposition. The modal responses, modal auto-correlation functions and discrete-time plant matrix (in state space modal form) are subsequently identified. System eigenvalues are computed from the plant matrix to obtain the natural frequencies and modal fractions of critical damping. Joint Approximate Diagonalization (JAD) of the Hankel matrices enables the under determined (more modes than sensors) problem to be effectively treated without restrictions on the number of sensors required. Because the analytic signal is used, the redundant complex conjugate pairs are eliminated, reducing the system order (number of modes) to be identified half. This enables smaller Hankel matrix sizes and reduced computational effort. The modal auto-correlation functions provide an expedient means of screening out spurious computational modes or modes corresponding to noise sources, eliminating the need for a consistency diagram. In addition, the reduction in the number of modes enables the modal responses to be identified when there are at least as many sensors as independent (not including conjugate pairs) modes. A further benefit of the algorithm is that identification of dissimilar left and right diagonalizers preclude the need for windowing of the analytic data. The effectiveness of the new modal identification method is demonstrated using vibration data from a 6 DOF simulation, 4-story building simulation and the Heritage court tower building.

A study and extension of second-order blind source separation to operational modal analysis

Second-order blind source separation (SOBSS) has gained recent interest in operational modal analysis (OMA), since it is able to separate a set of system responses into modal coordinates from which the system poles can be extracted by single-degree-of-freedom techniques. In addition, SOBSS returns a mixing matrix whose columns are the estimates of the system mode shapes. The objective of this paper is threefold. First, a theoretical analysis of current SOBSS methods is conducted within the OMA framework and its precise conditions of applicability are established. Second, a new separation method is proposed that fixes current limitations of SOBSS: It returns estimate of complex mode shapes, it can deal with more active modes than the number of available sensors, and it shows superior performance in the case of heavily damped and/or strongly coupled modes. Third, a theoretical connection is drawn between SOBSS and stochastic subspace identification (SSI), which stands as one of the points of reference in OMA. All approaches are finally compared by means of numerical simulations.

Intensive training induces longitudinal changes in meditation state-related EEG oscillatory activity

The capacity to focus one's attention for an extended period of time can be increased through training in contemplative practices. However, the cognitive processes engaged during meditation that support trait changes in cognition are not well characterized. We conducted a longitudinal wait-list controlled study of intensive meditation training. Retreat participants practiced focused attention (FA) meditation techniques for three months during an initial retreat. Wait-list participants later undertook formally identical training during a second retreat. Dense-array scalp-recorded electroencephalogram (EEG) data were collected during 6 min of mindfulness of breathing meditation at three assessment points during each retreat. Second-order blind source separation, along with a novel semi-automatic artifact removal tool (SMART), was used for data preprocessing. We observed replicable reductions in meditative state-related beta-band power bilaterally over anteriocentral and posterior scalp regions. In addition, individual alpha frequency (IAF) decreased across both retreats and in direct relation to the amount of meditative practice. These findings provide evidence for replicable longitudinal changes in brain oscillatory activity during meditation and increase our understanding of the cortical processes engaged during meditation that may support long-term improvements in cognition.

ICA-based and second-order separability of nonlinear models involving reference signals: General properties and application to quantum bits

Relatively few results have been reported about the separability of given classes of nonlinear mixtures by means of statistical criteria such as ICA. We here first prove the ICA separability of a wide class of nonlinear global (i.e. mixing+separating) models involving “reference signals”, i.e. unmixed signals. We also show the second-order separability of sub-classes of the above class of models. This work therefore concerns nonlinear extensions of (linear) adaptive noise cancellation. We illustrate the usefulness of our general results by applying them to a quantum information processing problem, which involves a model of Heisenberg-coupled quantum states (i.e. qubits). This paper opens the way to practical ICA-based and second-order blind source separation (BSS) methods for nonlinear mixtures encountered in various applications. These BSS methods are also outlined in this paper.

Quadratic optimization for simultaneous matrix diagonalization

Simultaneous diagonalization of a set of matrices is a technique that has numerous applications in statistical signal processing and multivariate statistics. Although objective functions in a least-squares sense can be easily formulated, their minimization is not trivial, because constraints and fourth-order terms are usually involved. Most known optimization algorithms are, therefore, subject to certain restrictions on the class of problems: orthogonal transformations, sets of symmetric, Hermitian or positive definite matrices, to name a few. In this paper, we present a new algorithm called QDIAG that splits the overall optimization problem into a sequence of simpler second order subproblems. There are no restrictions imposed on the transformation matrix, which may be nonorthogonal, indefinite, or even rectangular, and there are no restrictions regarding the symmetry and definiteness of the matrices to be diagonalized, except for one of them. We apply the new method to second-order blind source separation and show that the algorithm converges fast and reliably. It allows for an implementation with a complexity independent of the number of matrices and, therefore, is particularly suitable for problems dealing with large sets of matrices

On the use of simulated annealing to automatically assign decorrelated components in second-order blind source separation

In this paper, an automatic assignment tool, called BSS-AutoAssign, for artifact-related decorrelated components within a second-order blind source separation (BSS) is presented. The latter is based on the recently proposed algorithm dAMUSE, which provides an elegant solution to both the BSS and the denoising problem simultaneously. BSS-AutoAssign uses a local principal component analysis (PCA)to approximate the artifact signal and defines a suitable cost function which is optimized using simulated annealing. The algorithms dAMUSE plus BSS-AutoAssign are illustrated by applying them to the separation of water artifacts from two-dimensional nuclear overhauser enhancement (2-D NOESY) spectroscopy signals of proteins dissolved in water.

Second-Order Blind Separation of First- and Second-Order Cyclostationary Sources—Application to AM, FSK, CPFSK, and Deterministic Sources

Most of the second-order (SO) and higher order (HO) blind source separation (BSS) methods developed this last decade aim at blindly separating statistically independent sources that are assumed zero-mean, stationary, and ergodic. Nevertheless, in many situations of practical interest, such as in radiocommunications contexts, the sources are nonstationary and very often cyclostationary (digital modulations). The behavior of the current SO and fourth-order (FO) cumulant-based BSS methods in the presence of cyclostationary sources has been analyzed, recently, in a previous paper by Ferre/spl acute/ol and Chevalier, assuming zero-mean sources. However, some cyclostationary sources used in practical situations are not zero-mean but have a first-order (FIO) cyclostationarity property, which is, in particular, the case for some amplitude modulated (AM) signals and for some nonlinearly modulated digital sources such as frequency shift keying (FSK) or some continuous phase frequency shift keying (CPFSK) sources. For such sources, the results presented in the previous paper by Ferre/spl acute/ol and Chevalier no longer hold, and the purpose of this paper is to analyze the behavior and to propose adaptations of the current SO BSS methods for sources that are both FIO and SO cyclostationary and cyclo-ergodic. An extension for deterministic sources is also proposed in the paper.

Second Order Nonstationary Source Separation

This paper addresses a method of blind source separation that jointly exploits the nonstationarity and temporal structure of sources. The method needs only multiple time-delayed correlation matrices of the observation data, each of which is evaluated at different time-windowed data frame, to estimate the demixing matrix. The method is insensitive to the temporally white noise since it is based on only time-delayed correlation matrices (with non-zero time-lags) and is applicable to the case of either nonstationary sources or temporally correlated sources. We also discuss the extension of some existing methods with the overview of second-order blind source separation methods. Extensive numerical experiments confirm the validity and high performance of the proposed method.

On the behavior of current second and higher order blind source separation methods for cyclostationary sources

Most of the second-order (SO) and higher order (HO) blind source separation methods developed in the 1990s aim at blindly separating statistically independent sources that are assumed zero-mean, stationary, and ergodic. Nevertheless, in many situations of practical interest, such as in radiocommunication contexts, the sources are nonstationary and very often (quasi)-cyclostationary (digital modulations). In these conditions, it becomes important to wonder whether the performance of these current SO and HO blind source separation methods, which have been developed for stationary sources, may be affected by the potential nonstationarity of the latter. Limiting the analysis to the SO and fourth-order (FO) cumulant-based blind source separation methods, the purpose of this paper is to bring some answers to this important question through the behavior analysis of the empirical SO and FO cumulants estimator in the presence of zero-mean (quasi)-cyclostationary sources.