A weighted ℓ1 minimization algorithm for compressed sensing ECG

Compressive sensing has recently been applied to electrocardiogram (ECG) acquisition and reconstruction with the aim of lowering energy consumption and sampling rates in wireless body area networks for ambulatory ECG monitoring. However, most current methods only adopt a sparse prior on the ECG wavelet representation. In this paper, we propose to further exploit the wavelet representation structure by incorporating two properties in the formulation of the optimization problem: the exponentially decaying magnitude of the detail coefficients across scales and the accumulation of signal energy in the approximation subband. We derive a weighted ℓ₁ minimization algorithm, based on a maximum a posteriori (MAP) approach, that leads to a significant reduction in the number of measurements and superior reconstruction performance compared to current CS-based methods with application to wireless ECG systems.