Document Type : Original Article

Author

• THOMAS SCHANZE

Institute for Biomedical Engineering, Faculty of Life Science Engineering (LSE), Technische Hochschule Mittelhessen (THM) - University of Applied Sciences, Germany

Abstract

The electrocardiogram (ECG) is an important diagnostic tool in medicine. During a recording, ECG waveforms may change due to intrinsic processes, changes in recording parameters, such as recording electrode properties, and especially artefacts, e.g., electromagnetic hum or noise. Clearly, signal distortion can adversely affect medical decisions. In recent years, a variety of signal processing methods have been introduced to remove noise from signals. One of these methods is singular value decomposition (SVD)-based denoising, in which QRS-aligned sections of a signal channel are arranged in a matrix, which is then decomposed into singular values and left and right singular vectors. However, the right combination of these components can result in surprisingly good noise reduction. For multichannel recordings, this approach can be applied to each single channel. This means that cross-channel correlations, i.e., signal correlations between channels, cannot be used. An obvious extension for the analysis of QRS-aligned multichannel signal sections is their representation by a three-dimensional array, i.e., a third-order tensor with the dimensions time, segment and channel. Here, we show how to denoise tensorized QRS-aligned multichannel ECG sections, each comprising P-wave, QRS-complex, and T-wave, by higher-order singular value decomposition (HOSVD). We present a method for combining HOSVD components for denoising, i.e., noise reduction. Furthermore, we show that not only noise reduction but also data compression can be achieved with this method. Denoising quality is evaluated by using the Pearson correlation coefficient and extended Frobenius norm calculated for noisy and original and also for denoised and original signals. Gaussian white noise was used for the contamination of the original multichannel recordings, resulting in test data with various signal-to-noise ratios. The compression ratio determines the compression performance. With the proposed method, the correlations between the noisy and the original signal and the denoised signal with the original signal could be increased significantly, e.g., from around 0.45 to 0.97, and this at a compression rate of around 127. However, the tensor decomposition-based noise reduction of multiple channels often yields better results than the SVD-based single-channel denoising. This is the case when there are correlations between the channels in the multichannel signal to be denoised, especially correlations in the wanted signals. A scenario with more realistic noise conditions was generated by using an ECG simulator to further analyze the properties of HOSVD-based compression and denoising. This led to the finding that the selection of the HOSVD computed reconstruction components required for denoising needs to be done carefully. To conclude, tensor decomposition-based compression and denoising can be an appropriate tool for the compression and denoising of multichannel signals. However, its usefulness under real-world conditions has yet to be demonstrated.

Keywords

• Biosignal
• Compression
• Denoising
• Signal processing
• Singular value decomposition
• Tensor decomposition