The power of tensors in cardiac applications

The electrocardiogram (ECG) is a biomedical signal that is widely used to monitor the heart and diagnose cardiac problems. Depending on the clinical need, the ECG is recorded with one or multiple leads (or channels) from different body locations. The signals from different ECG leads represent the cardiac activity in different spatial directions and are thus complementary to each other. In traditional methods, the ECG signal is represented as a vector or a matrix and processed to analyze temporal information. When multiple leads are present, most methods process each lead individually and combine decisions from all leads in a later stage. While this approach is popular, it fails to exploit the structural information captured by the different leads.

The use of tensors allows the analysis of multiple modes simultaneously, using both temporal and spatial information. Tensor decomposition methods have been applied on ECG signals to solve different clinical challenges. We discuss the power of tensor-based methods for different ECG appications through various examples. In order to highlight the exible nature of tensor-based methods, we showcase various ways to construct and decompose tensors, depending on the signal characteristics and the particular application.