The estimation of the atrial activity (AA) signal from electrocardiogram (ECG) recordings is an important step in the noninvasive analysis of atrial fibrillation (AF), the most common sustained arrhythmia encountered in clinical practice. This problem admits a blind source separation (BSS) formulation that has been recently posed as a tensor factorization, using the Hankel-based block term decomposition (BTD), which is particularly well-suited to the estimation of exponential models like AA during AF. However, persistent forms of AF are characterized by short R-R intervals and very disorganized (or weak) AA, making it difficult to model AA directly and perform its successful extraction through Hankel-BTD. To overcome this drawback, the present work proposes a tensor approach to estimate QRS complexes and subtract them from the ECG, resulting in a signal that, ideally, only contains the AA component. Such an approach tackles the problem of blind separation of rational functions, which models QRS complexes explicitly. The data tensor admitting a BTD is built from Löwner matrices generated from each lead of the observed ECG. To this end, this paper formulates a variant of the recently proposed constrained alternating group lasso (CAGL) algorithm that imposes Löwner structure on the decomposition blocks. This is done by performing an orthogonal projection, which we explicitly derive, at each iteration of CAGL. Results from experiments with synthetic data show the consistency of the proposed Löwner-constrained AGL (LCAGL) in extracting the desired sources. Experimental results obtained on a population of 20 patients suffering from persistent AF show that the proposed variant outperforms other tensor-based methods in terms of atrial signal estimation quality from ECG records as short as a single heartbeat.

The Fukunaga-Koontz transform (FKT) is a powerful supervised feature extraction method used in two-class recognition problems, particularly when the classes have equal mean vectors but different covariance matrices. The present work proves that it is also possible to perform the FKT in an unsupervised manner, sparing the need for labeled data, by using a variant of L1-norm Principal Component Analysis (L1-PCA) that minimizes the L1-norm in the feature space. Rigorous proof is given in the case of data drawn from a mixture of Gaussians. A working iterative algorithm based on gradient-descent in the Stiefel manifold is put forward to perform L1-norm minimization with orthogonal constraints. A number of numerical experiments on synthetic and real data confirm the theoretical findings and the good convergence characteristics of the proposed algorithm.

Respiratory patterns are commonly measured to monitor and diagnose cardiovascular, metabolic, and sleep disorders. Electronic devices such as masks used to record respiratory waveforms usually require medical staff support and obstruct the patients' breathing, causing discomfort. New techniques are being investigated to overcome such limitations. An emerging approach involves accelerometers to estimate the respiratory waveform based on chest motion. However, most of the existing techniques employ a single accelerometer placed on an arbitrary thorax position. The present work investigates the use and optimal placement of multiple accelerometers located on the thorax and the abdomen. The study population is composed of 30 healthy volunteers in three different postures. By means of a custom-made microcontrolled system, data are acquired from an array of ten accelerometers located on predefined positions and a pneumotachograph used as reference. The best sensor locations are identified by optimal linear reconstruction of the reference waveform from the accelerometer data in the minimum mean square error sense. The analysis shows that right-hand side locations contribute more often to optimal respiratory waveform estimates, a sound finding given that the right lung has a larger volume than the left lung. In addition, we show that the respiratory waveform can be blindly extracted from the recorded accelerometer data by means of independent component analysis. In conclusion, linear processing of multiple accelerometers in optimal positions can successfully recover respiratory information in clinical settings, where the use of masks may be contraindicated.

Principal component analysis (PCA) based on L1-norm maximization is an emerging technique that has drawn growing interest in the signal processing and machine learning research communities, especially due to its robustness to outliers. The present work proves that L1-norm PCA can perform independent component analysis (ICA) under the whitening assumption. However, when the source probability distributions fulfil certain conditions, the L1-norm criterion needs to be minimized rather than maximized, which can be accomplished by simple modifications on existing optimal algorithms for L1-PCA. If the sources have symmetric distributions, we show in addition that L1-PCA is linked to kurtosis optimization. A number of numerical experiments illustrate the theoretical results and analyze the comparative performance of different algorithms for ICA via L1-PCA. Although our analysis is asymptotic in the sample size, this equivalence opens interesting new perspectives for performing ICA using optimal algorithms for L1-PCA with guaranteed global convergence while inheriting the increased robustness to outliers of the L1-norm criterion.

Despite the increasing popularity of catheter ablation (CA) for treating atrial fibrillation (AF), the identification of patients who would actually benefit from the therapy remains a challenging open issue. This study aims at noninvasively predicting CA outcome by quantifying the spatio-temporal variability of the atrial activity (AA) signal measured on the standard 12-lead electrocardiogram. The normalized mean square error (NMSE) between consecutive atrial segments and their principal component approximations is computed for each lead, as a recent noninvasive index of AF organization. In the present work, the multilead NMSE array is decomposed by means of a nonnegative matrix factorization (NNMF) with two different initializations. The reconstruction error between the original NMSE matrix and its low-rank NNMF approximation is taken as a classification feature. A dataset of persistent AF patients undergoing CA reveals that the proposed feature is able to predict the therapy outcome with a notably higher level of statistical significance than recent single-lead indices.

Abstract The popular Alamouti orthogonal space time code attains full transmit diversity in multiple antenna systems. This paper addresses the problem of blind channel identification in (2 × 1) Alamouti coded systems. Under the assumption of independent symbol substreams, the channel can be estimated from the eigendecomposition of matrices composed of second‐ or higher‐order statistics (cumulants) of the received signal. The so‐called joint approximate diagonalization of eigenmatrices (JADE) method for blind source separationviaindependent component analysis is optimal in that it tries to simultaneously diagonalize a full set of fourth‐order cumulant matrices. To reduce computational complexity, we perform the eigenvalue decomposition of a single cumulant matrix, which is judiciously chosen by maximizing its expected eigenvalue spread. Simulation results show that the resulting technique outperforms existing blind Alamouti channel estimation methods and achieves a performance close to JADE's at a fraction of the computational cost. Copyright © 2010 John Wiley & Sons, Ltd.

IAM ABOUT to start my second year of service as the Editor-in-Chief (EiC) of the IEEE TRANSACTIONS ON NEURAL NETWORKS (TNN). Needless to say, my first year as the EiC has been full of excitement and challenges. Transitioning this position from my predecessor to me went very smoothly during the months of September 2009 to January 2010. During the past year, we have accumulated 50+ Associate Editors (AEs) handling roughly 600 new submissions (not counting resubmissions and revised submissions). With the help of these AEs and my predecessor, I was quickly able to learn to do my job, and as such, the transition had very few glitches. The easy part of my job is checking whether a submission is in compliance with our guidelines and where it is within the scope of the TRANSACTIONS, before it is assigned to an AE for handling. The difficult part of my job has been dealing with some papers with three or more reviewers, all of whom agreed to review them but for some reason failed to respond to repeated automatic-review reminders. AEs handling these papers have to take several extra steps to remind reviewers through phone calls or e-mails, look for replacement reviewers, or review the papers themselves. Most authors have been appreciative of the work of the AEs and reviewers, and they accept our decisions without a problem. The backlog of papers has been kept short over the last year. We have maintained an organized printing and paperacceptance schedule, with papers typically printed in the journal within 2‐3 months of acceptance. Our page budget has been kept constant in the past few years (roughly 2060 pages per year), and we expect to hold the same page count for next year.

Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the independent components one after another. A novel method for deflationary ICA, referred to as RobustICA, is put forward in this paper. This simple technique consists of performing exact line search optimization of the kurtosis contrast function. The step size leading to the global maximum of the contrast along the search direction is found among the roots of a fourth-degree polynomial. This polynomial rooting can be performed algebraically, and thus at low cost, at each iteration. Among other practical benefits, RobustICA can avoid prewhitening and deals with real- and complex-valued mixtures of possibly noncircular sources alike. The absence of prewhitening improves asymptotic performance. The algorithm is robust to local extrema and shows a very high convergence speed in terms of the computational cost required to reach a given source extraction quality, particularly for short data records. These features are demonstrated by a comparative numerical analysis on synthetic data. RobustICA's capabilities in processing real-world data involving noncircular complex strongly super-Gaussian sources are illustrated by the biomedical problem of atrial activity (AA) extraction in atrial fibrillation (AF) electrocardiograms (ECGs), where it outperforms an alternative ICA-based technique.

This brief deals with the problem of blind source separation (BSS) via independent component analysis (ICA). We prove that a linear combination of the separator output fourth-order marginal cumulants (kurtoses) is a valid contrast function for ICA under prewhitening if the weights have the same sign as the source kurtoses. If, in addition, the source kurtoses are different and so are the linear combination weights, the contrast eliminates the permutation ambiguity typical to ICA, as the estimated sources are sorted at the separator output according to their kurtosis values in the same order as the weights. If the weights equal the source kurtoses, the contrast is a cumulant matching criterion based on the maximum-likelihood principle. The contrast can be maximized by means of a cost-efficient Jacobi-type pairwise iteration. In the real-valued two-signal case, the asymptotic variance of the resulting Givens angle estimator is determined in closed form, leading to the contrast weights with optimal finite-sample performance. A fully blind solution can be implemented by computing the optimum weights from the initial source estimates obtained by a classical ICA stage. An experimental study validates the features of the proposed technique and shows its superior performance compared to related previous methods.

A contrast function for independent component analysis (ICA) is presented incorporating the prior knowledge on the sub-Gaussian or super-Gaussian character of the sources as described by their kurtosis signs. The contrast is related to the maximum likelihood principle, reduces the permutation indeterminacy typical of ICA, and proves particularly useful in the direct extraction of a source signal with distinct kurtosis sign. In addition, its numerical maximization can be performed cost-effectively by a Jacobi-like pairwise iteration. Extensions to standardized cumulants of orders other than four are also given.

The step size leading to the absolute minimum of the constant modulus (CM) criterion along the search direction can be obtained algebraically at each iteration among the roots of a third-degree polynomial. The resulting optimal step-size CMA (OS-CMA) is compared with, other CM-based iterative techniques in terms of performance-versus-complexity trade-off.

Channel equalization is an important problem in digital communications. The paper studies a hybrid equalization criterion combining the constant modulus (CM) property and the minimum mean square error (MMSE) between the equalizer output and the known pilot sequence. An efficient semi-blind block gradient-descent algorithm is proposed, in which the step size globally minimizing the cost function along the search direction is algebraically computed at each iteration. The use of the optimal step size notably accelerates convergence and can further reduce the impact of local extrema on the semi-blind algorithm's performance. The proposed approach is not restricted to the CM-MMSE principle, but it can benefit other equalization criteria as well.

This contribution provides a unified framework for the analytic or closed-form estimators for blind separation of independent source signals in real-valued instantaneous linear mixtures, in the noiseless two-source two-sensor scenario. First, the connections among three existing 4th-order analytic formulae (CF, AML and EML) are clarified. Next, a general expression for the estimation of the relevant separation parameter from the data nth-order statistics is unveiled, of which the extended maximum likelihood (EML) estimator is a particular case at n=4, and from which a novel third-order estimator is derived at n=3. Asymptotic performance analysis results are also presented. Associated contrast-function optimization criteria are shown to extend the applicability of a known 4th-order contrast function in the two-signal case. Simulations illustrate and validate the theoretical exposition.

Blind source separation aims to extract a set of independent signals from a set of observed linear mixtures. After whitening the sensor output, the separation is achieved by estimating an orthogonal transformation, which in the real-mixture two-source two-sensor case is entirely characterized by a single rotation angle. This contribution studies an estimator of such an angle. Even though it is derived from geometric notions based on the scatter-plots of the signals involved, it is found, empirically, to exhibit a performance clearly up to the mark of other methods based on optimality criteria and, theoretically, to improve and generalize one of such procedures. The simplicity of the suggested estimator results in a straightforward adaptive version, which converges regardless of the source distribution, for quite mild conditions, and whose asymptotic analysis is easy to carry out. The applicability of the estimator in a full separation system is also illustrated.

Several methods based on higher order statistics are currently used to solve the blind source separation (BSS) problem. In the present letter an approach from Mansour and Jutten (1995) is considered and simplified via the application of the singular value decomposition, which decorrelates the observed signals and leads to a straightforward solution based on some results developed by Comon (1989).