Vicente Zarzoso

Noninvasive fetal electrocardiogram extraction: blind separation versus adaptive noise cancellation

The problem of the fetal electrocardiogram (FECG) extraction from maternal skin electrode measurements can be modeled from the perspective of blind source separation (BSS). Since no comparison between BSS techniques and other signal processing methods has been made, the authors compare a BSS procedure based on higher-order statistics and Widrows multireference adaptive noise cancelling approach. As a best-case scenario for this latter method, optimal Wiener-Hopf solutions are considered. Both procedures are applied to real multichannel ECG recordings obtained from a pregnant woman. The experimental outcomes demonstrate the more robust performance of the blind technique and, in turn, verify the validity of the BSS model in this important biomedical application.

Atrial activity extraction for atrial fibrillation analysis using blind source separation

This contribution addresses the extraction of atrial activity (AA) from real electrocardiogram (ECG) recordings of atrial fibrillation (AF). We show the appropriateness of independent component analysis (ICA) to tackle this biomedical challenge when regarded as a blind source separation (BSS) problem. ICA is a statistical tool able to reconstruct the unobservable independent sources of bioelectric activity which generate, through instantaneous linear mixing, a measurable set of signals. The three key hypothesis that make ICA applicable in the present scenario are discussed and validated: 1) AA and ventricular activity (VA) are generated by sources of independent bioelectric activity; 2) AA and VA present non-Gaussian distributions; and 3) the generation of the surface ECG potentials from the cardioelectric sources can be regarded as a narrow-band linear propagation process. To empirically endorse these claims, an ICA algorithm is applied to recordings from seven patients with persistent AF. We demonstrate that the AA source can be identified using a kurtosis-based reordering of the separated signals followed by spectral analysis of the sub-Gaussian sources. In contrast to traditional methods, the proposed BSS-based approach is able to obtain a unified AA signal by exploiting the atrial information present in every ECG lead, which results in an increased robustness with respect to electrode selection and placement.

Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast With Algebraic Optimal Step Size

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. RobustICAs 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.

Spatiotemporal blind source separation approach to atrial activity estimation in atrial tachyarrhythmias

The analysis and characterization of atrial tachyarrhythmias requires, in a previous step, the extraction of the atrial activity (AA) free from ventricular activity and other artefacts. This contribution adopts the blind source separation (BSS) approach to AA estimation from multilead electrocardiograms (ECGs). Previously proposed BSS methods for AA extraction-e.g., independent component analysis (ICA)-exploit only the spatial diversity introduced by the multiple spatially-separated electrodes. However, AA typically shows certain degree of temporal correlation, with a narrowband spectrum featuring a main frequency peak around 3.5-9 Hz. Taking advantage of this observation, we put forward a novel two-step BSS-based technique which exploits both spatial and temporal information contained in the recorded ECG signals. The spatiotemporal BSS algorithm is validated on simulated and real ECGs from a significant number of atrial fibrillation (AF) and atrial flutter (AFL) episodes, and proves consistently superior to a spatial-only ICA method. In simulated ECGs, a new methodology for the synthetic generation of realistic AF episodes is proposed, which includes a judicious comparison between the known AA content and the estimated AA sources. Using this methodology, the ICA technique obtains correlation indexes of 0.751, whereas the proposed approach obtains a correlation of 0.830 and an error in the estimated signal reduced by a factor of 40%. In real ECG recordings, we propose to measure performance by the spectral concentration (SC) around the main frequency peak. The spatiotemporal algorithm outperforms the ICA method, obtaining a SC of 58.8% and 44.7%, respectively.

Blind Source Separation

A myriad of applications require the extraction of a set of signals which are not directly accessible. Instead, this extraction must be carried out from another set of measurements which were generated as mixtures of the initial set. Since usually neither the original signals — called sources — nor the mixing transformation are known, this is certainly a challenging problem of multichannel blind estimation. One of the most typical examples is the socalled “ cocktail party” problem. In this situation, any person attending the party can hear the speech of the speaker they want to listen to, together with surrounding sounds coming from other ’ competing’ speakers, music, background noises, etc. Everybody has experienced how the human brain is able to separate all these incoming sound signals and to ’ switch’ to the desired one. Similar results can be achieved by adequately processing the output signals of an array of microphones, as long as the signals to be extracted fulfil certain conditions [62, 63] . Wireless communications is another usual application field of signal separation techniques. In a CDMA (Code Division Multiple Access) environment several users share the same radio channel by transmitting their signal after modifying it according to an appropriate code. Traditionally, the extraction of the desired signal at the receiving end requires the knowledge of the corresponding code.

Blind separation of independent sources for virtually any source probability density function

The blind source separation (BSS) problem consists of the recovery of a set of statistically independent source signals from a set of measurements that are mixtures of the sources when nothing is known about the sources and the mixture structure. In the BSS scenario, of two noiseless real-valued instantaneous linear mixtures of two sources, an approximate maximum-likelihood (ML) approach has been suggested in the literature, which is only valid under certain constraints on the probability density function (pdf) of the sources. In the present paper, the expression for this ML estimator is reviewed and generalized to include virtually any source distribution. An intuitive geometrical interpretation of the new estimator is also given in terms of the scatter plots of the signals involved. An asymptotic performance analysis is then carried out, yielding a closed-form expression for the estimator asymptotic pdf. Simulations illustrate the behavior of the suggested estimator and show the accuracy of the asymptotic analysis. In addition, an extension of the method to the general BSS scenario of more than two sources and two sensors is successfully implemented.

Atrial activity extraction based on blind source separation as an alternative to QRST cancellation for atrial fibrillation analysis

Atrial fibrillation (AF) characterization from electrocardiogram (ECG) recordings requires the elimination of ventricular activity (VA). The present contribution demonstrates the potential of blind source separation (BSS) in atrial activity (AA) extraction from AF episodes, The applicability of BSS techniques relies on the assumption that AA and VA are decoupled, and hence can be regarded as generated by independent bioelectric sources. In the comparative experiments, a multi-lead AF signal model is synthesized by adding real AA from AF episodes to ECGs recorded from healthy patients. Two direct QRST-cancellation methods are also considered, template matching and subtraction, and adaptive noise cancellation. Further experiments are performed on real multi-lead recordings from 20 patients with AF episodes. The BSS approach shows a superior performance, thus manifesting the suitability of BSS techniques for AA extraction. As a favourable by-product, BSS arises as a novel technique for QRST-complex cancellation.

Optimal Step-Size Constant Modulus Algorithm

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.

Adaptive blind source separation for virtually any source probability density function

Blind source separation (BSS) aims to recover a set of statistically independent source signals from a set of linear mixtures of the same sources. In the noiseless real-mixture two-source two-sensor scenario, once the observations are whitened (decorrelated and normalized), only a Givens rotation matrix remains to be identified in order to achieve the source separation. In this paper an adaptive estimator of the angle that characterizes such a rotation is derived. It is shown to converge to a stable valid separation solution with the only condition that the sum of source kurtosis be distinct from zero. An asymptotic performance analysis is carried out, resulting in a closed-form expression for the asymptotic probability density function of the proposed estimator. It is shown how the estimator can be incorporated into a complete adaptive source separation system by combining it with an adaptive prewhitening strategy and how it can be useful in a general BSS scenario of more than two signals by means of a pairwise approach. A variety of simulations assess the accuracy of the asymptotic results, display the properties of the estimator (such as its robust fast convergence), and compare this on-line BSS implementation with other adaptive BSS procedures.

Blind and semi-blind equalization based on the constant power criterion

This paper focuses on the constant power (CP) criterion for blind linear equalization of digital communication channels. This recently proposed criterion is specially designed for the extraction of q-ary phase shift keying (q-PSK) signals using finite impulse response equalizers. When zero-forcing equalizers exist, the CP cost function accepts exact analytic solutions that are unaffected by undesired local extrema and spare costly iterative optimization. A subspace-based method exploiting the Toeplitz-like structure of the solution space is put forward to recover the minimum-length equalizer impulse response from the overestimated-length solutions. The proposed method is more robust to the relative weights of the minimum-length equalizer taps than existing techniques. In less ideal scenarios where the analytic solutions are only approximate minimizers of the criterion, a gradient-descent algorithm is proposed to minimize the cost function. To reduce the detrimental effects of suboptimal equilibria and accelerate convergence, the iterative algorithm is initialized with the approximate closed-form solution, and an optimal step size is incorporated into its updating rule. This optimal step size, which globally minimizes the cost function along the search direction, can be computed algebraically. A semi-blind implementation, which is useful when training data are available, further reduces the impact of undesired local extrema and enhances the convergence characteristics (particularly the robustness to the equalizer initialization) of the iterative algorithm from just a few pilot symbols. All these beneficial features are demonstrated with an experimental study of the proposed CP-based methods in a variety of channels and simulation conditions.