TensorECG: Adaptive-Rank Temporal–Spatial Tensor Compression of Multi-lead ECG Signals with Wavelet and low bit residual refinement

Abstract The rapid growth of long-duration ECG recordings from wearable and ambulatory monitors has created a compression bottleneck for wireless transmission and storage. Existing block- and transform-based methods largely exploit redundancy along only one or two dimensions, offering limited joint modeling of inter-beat and inter-lead correlations. TensorECG addresses this gap by introducing a three-way tensor representation for multi-lead ECG that extends conventional matrix-based approaches to three physiologically meaningful axes: a temporal axis capturing self-similarity across successive heartbeats, a spatial axis capturing inter-lead correlations arising from different projections of cardiac electrical activity, and a morphological axis representing individual beat waveform shapes. A discrete wavelet transform is applied to each beat prior to tensorization, concentrating signal energy into few significant coefficients and reducing the effective dimensionality of the morphological axis. These three dimensions are jointly represented in a unified tensor rather than modeled separately, and the resulting coefficient tensor is compressed via rank-r Tensor-Train SVD, jointly capturing beat and lead correlations. TT-core coefficients are entropy coded, with an optional low-bit residual-refinement layer entropy-coding reconstruction error for additional rate–fidelity control. TT-rank, the key sensitive hyperparameter, is tuned once on a 35-record MIT-BIH training split and fixed for testing on a held-out split and three PhysioNet databases (2–15 leads, 250–1000 Hz). An adaptive-rank DWT+TT variant achieves compression ratios of 18.9–51.6 across 4–12\% PRD targets and clinical validation showing sub-millivolt amplitude and sub-millisecond interval errors