Marian Kotas

Application of projection pursuit based robust principal component analysis to ECG enhancement

Abstract The paper presents an application of principal component analysis (PCA) to ECG processing. For this purpose the ECG beats are time-aligned and stored in the columns of an auxiliary matrix. The matrix, considered as a set of multidimensional variables, undergoes PCA. Reconstruction of the respective columns on the basis of a low dimensional principal subspace leads to the enhancement of the stored ECG beats. A few modifications of this classical approach to ECG signal filtering by means of a multivariate analysis are introduced. The first one is based on replacing the classical PCA by its robust extension. The second consists in replacing the analysis of the whole synchronized beats by the analysis of shorter signal segments. This creates the background for the third modification, which introduces the concept of variable dimensions of the subspaces corresponding to different parts of ECG beats. The experiments performed show that introduction of the respective modifications significantly improves the classical approach to ECG processing by application of principal component analysis.

Towards noise immune detection of fetal QRS complexes

The noninvasive fetal electrocardiography is a source of more precise information on the fetal heart activity than the measurements based on Doppler ultrasound signals. However, the clinical diagnostic applications of this technique are limited by difficulty with successful detection of small amplitude fetal QRS complexes. In this study, we investigate the influence of different stages of fetal signals processing on the detection performance. The main propositions of the paper are: application of normalized matched filtering to fetal QRS complexes enhancement and a new approach to the final detection of the complexes. Compared to the classical detectors, the proposed new one allows a significant increase of the detection performance for signals of very different quality.

Application of spatio-temporal filtering to fetal electrocardiogram enhancement

In this paper we propose a new structure of the instrumentation for electrocardiographic fetal monitoring. We apply a single-channel approach to maternal electrocardiogram suppression in the recorded four abdominal bioelectric signals. Then we exploit spatial and temporal properties of the extracted four-channel fetal electrocardiogram to construct a new channel with higher signal-to-noise ratio. Finally, we perform detection of fetal QRS complexes. The proposed approach is investigated with the help of the constructed database of the maternal abdominal signals. During the detection tests, the spatio-temporal filtering allowed us to decrease significantly the number of the detection errors of different detectors applied. Moreover, we present visually that even if the fetal QRS complexes are buried in noise, the spatio-temporal filtering can produce the signal with the discernible ones.

Projective filtering of time-aligned ECG beats

A method of electrocardiographic (ECG) signal processing developed by introduction of time synchronization into the method of nonlinear state-space projections is presented. It can be regarded as an extension of time averaging but contrary to usual averaging it preserves variability of ECG beats morphology. For this purpose, after the respective beats time alignment, the synchronized intervals of the signal undergo processing according to the rules of principal component analysis (PCA). PCA allows for determination of orthogonal basis functions which can be employed for approximation of the respective intervals. The operation is aimed to retain the deviations from the mean which result from the desired component changes and to reject the deviations caused by noise. The methods capabilities are investigated and some of its applications are presented.

Detection of low amplitude fetal QRS complexes

The significance of the most important operations performed by the noninvasive systems for fetal heart rate determination is investigated. The method of template subtraction for maternal ECG suppression is compared to the method based on independent component analysis. The QRS detector based on the classical slope-responsive preprocessing competes with the one that employs normalized matched filtering for QRS enhancement. A small database containing the four-channel abdominal ECG signals with the marked positions of the fetal QRS complexes is prepared to enable the investigations. The performed experiments show the factors that have the greatest impact on the results of the fetal QRS detection, and an effective approach to cope the problem is proposed.

Averaging of nonlinearly aligned signal cycles for noise suppression

Abstract Averaging of nonlinearly aligned (time-warped) signal cycles is an important method for suppressing noise of quasi-periodical or event related signals. However, in the paper we show that the operation of time warping introduces unfavorable violation of the requirements that should be satisfied for effective averaging and, as a result, it causes poor suppression of noise. To limit these effects, we redefine the matrix of the alignment costs. To improve results of averaging in cases of variable energy noise, we apply weighting of the summed signal samples. The derived formula gives smaller weights for more noisy signal cycles and this way limits their influence on the constructed template. The proposed modifications caused a significant increase of the Noise Reduction Factor (NRF) in the experiments on the simulated evoked potentials. Whereas the greatest NRF obtained by the reference methods in nonstationary white noise environment was equal to 1.55, for the new method proposed we achieved a value of 4.44. For non-stationary colored noise, the corresponding values were 1.44 and 2.99. Moreover, application of the developed method to ECG signal processing, prior to the measurements of the QT interval, significantly improved the measurements immunity to noise.

Telemedical application for centralized home care of high-risk pregnancy based on control sharing approach

The paper presents a fetal telemonitoring system, where the signals are acquired remotely at patient’s home using portable antepartum fetal monitor, and wirelessly transmitted to the central computer through the GSM network. The external telemedical channels were developed as a part of the centralized fetal monitoring system, whose architecture was extended by set of mobile instrumentation. While within a classical centralized fetal surveillance system all control functions are carried out from the central station, for remote monitoring the functions have to be shared between the hospital and the patient’s side. Some aspects of the system design allowing for optimal usage of existing structure and service procedures, and for being more patient-friendly and cost-effective, are discussed.

On robust fuzzy c-regression models

One of the most popular clustering methods based on minimization of a criterion function is the fuzzy c-means one. Its generalization by application of hyperplane shaped prototypes of the clusters is known as the Fuzzy C-Regression Models (FCRM) method. Although with this generalization many new applications of clustering emerged, it appeared to be rather sensitive to poor initialization and to the presence of noise and outliers in data. In this paper we introduce a new objective function, using the Hubers M-estimators and the Yagers OWA operators to overcome the disadvantages of the approach considered. We derive and describe an algorithm for minimization of the objective function defined. We have called it the Fuzzy C-Ordered-Regression Models (FCORM) clustering algorithm. The algorithm is compared to a few other important reference ones. To this end experiments on synthetic data with various types of noise and different numbers of outliers are carried out. We investigate the methods performance in the conditions that can be encountered in signal analysis. Large-scale simulations demonstrate the competitiveness and usefulness of the method proposed.

Hierarchical clustering with planar segments as prototypes

Abstract Clustering methods divide a set of observations into groups in such a way that members of the same group are more similar to one another than to the members of the other groups. One of the scientifically well known methods of clustering is the hierarchical agglomerative one. For data of different properties different clustering methods appear favorable. If the data possess locally linear form, application of planar (or hyperplanar) prototypes should be advantageous. However, although a clustering method using planar prototypes, based on a criterion minimization, is known, it has a crucial drawback. It is an infinite extent of such prototypes that can result in addition of very distant data points to a cluster. Such distant points can considerably differ from the majority within a cluster. The goal of this work is to overcome this problem by developing a hierarchical agglomerative clustering method that uses the prototypes confined to the segments of hyperplanes. In the experimental part, we show that for data that possess locally linear form this method is highly competitive to the method of the switching regression models (the accuracy improvement of 24%) as well as to other well-known clustering methods (the accuracy improvement of 16%).

Dynamic Time Warping Based on Modified Alignment Costs for Evoked Potentials Averaging

Averaging of time-warped signal cycles is an important tool for suppressing noise of quasi-periodic or event related signals. However, in the paper we show that the operation of time warping introduces unfavorable correlation among the noise components of the summed cycles. Such correlation violates the requirements necessary for effective averaging and results in poor suppression of noise. To limit these effects, we redefine the matrix of the alignment costs. The proposed modifications result in significant increase of the noise reduction factor in the experiments on different types and levels of noise.