Tensor decomposition-based compression and noise reduction of multichannel ECG signals

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,