Abstract
The electrocardiogram (ECG) follows a characteristic shape, which has led to the development of several mathematical models for extracting clinically important information. Our main objective is to resolve limitations of previous approaches, that means to simultaneously cope with various noise sources, perform exact beat segmentation, and to retain diagnostically important morphological information. We therefore propose a model that is based on Hermite and sigmoid functions combined with piecewise polynomial interpolation for exact segmentation and low-dimensional representation of individual ECG beat segments. Hermite and sigmoidal functions enable reliable extraction of important ECG waveform information while the piecewise polynomial interpolation captures noisy signal features like the baseline wander (BLW). For that we use variable projection, which allows the separation of linear and nonlinear morphological variations of the according ECG waveforms. The resulting ECG model simultaneously performs BLW cancellation, beat segmentation, and low-dimensional waveform representation. We demonstrate its BLW denoising and segmentation performance in two experiments, using synthetic and real data. Compared to state-of-the-art algorithms, the experiments showed less diagnostic distortion in case of denoising and a more robust delineation for the P and T wave. This work suggests a novel concept for ECG beat representation, easily adaptable to other biomedical signals with similar shape characteristics, such as blood pressure and evoked potentials. Our method is able to capture linear and nonlinear wave shape changes. Therefore, it provides a novel methodology to understand the origin of morphological variations caused, for instance, by respiration, medication, and abnormalities.
Highlights
T HE electrocardiogram (ECG) is doubtlessly the most widely used biomedical signal for cardiac diagnosis
The scatter quantified by the inter quartile range (IQR) was the smallest in our case for all quality criteria, which indicates that our method is the most robust in different scenarios of baseline noise
We have illustrated that the combination of adaptive Hermite and sigmoidal functions with spline interpolation successfully copes with the challenges faced in ECG signal processing
Summary
T HE electrocardiogram (ECG) is doubtlessly the most widely used biomedical signal for cardiac diagnosis. It is measured by recording the potential difference between electrodes placed on standardized locations on the surface of the body. Are these parameters relevant, their development over time, their beat-to-beat or long-term fluctuations, their responses to heart rate changes, and the interplay between them may be of great clinical interest [3]. This gives raise to two major challenging tasks from a signal processing point of view: denoising and wave segmentation
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