Investigation of Kronecker-Based Recovery of Compressed ECG Signal

Continuous measurement of electrocardiogram (ECG) signal is required for detecting various cardiac abnormalities, such as arrhythmia. Wearable devices have become ubiquitous as continuous monitoring devices. Due to power and memory restrictions in wearable devices, signal acquisition may need to be done in smaller segments using compressive sensing (CS) techniques. However such acquisitions may lead to poor recovery of compressed measurements. A Kronecker-based novel recovery technique has been recently proposed to improve the recovery of compressed signals where the recovery is achieved through a single recovery of concatenated compressed signal segments. In this article, a mathematical reasoning for improvement using the Kronecker-based recovery over standard CS recovery procedure is presented. A detailed investigation of Kronecker-based recovery technique of compressed ECG signal is presented using ECG signals from MIT-BIH Arrhythmia Database. As a part of this investigation, the quality of recovery with random and deterministic sensing of ECG signals and impact of choice of sparsifying dictionaries under various compression ratios (CRs) are considered. Deterministic sensing with deterministic binary block diagonal (DBBD) matrix and discrete cosine transform (DCT) as sparsifying basis is seen to provide the best recovery for ECG signals. Kronecker-based recovery of noisy ECG signals is possible with DBBD measurement matrix.