Multichannel Electrocardiogram Reconstruction in Wireless Body Sensor Networks Through Weighted $\ell_{1,2}$ Minimization

The emerging compressive sensing (CS) paradigm holds considerable promise for improving the energy efficiency of wireless body sensor networks, which enables nodes to employ a sample rate significantly below Nyquist while still able to accurately reconstruct signals. In this paper, we propose a weighted $\ell _{1,2}$ minimization method for multichannel electrocardiogram (ECG) reconstruction by exploiting both the interchannel correlation and multisource prior in wavelet domain. A sufficient and necessary condition for exact recovery via the proposed method is derived. Based upon the condition, the performance gain of the proposed method is analyzed theoretically. Furthermore, a reconstruction error bound of the proposed method is obtained, which indicates that the proposed method is stable and robust in recovering sparse and compressible signals from noisy measurements. Extensive experiments utilizing Physikalisch-Technische Bundesanstalt diagnostic ECG database and open-source electrophysiological toolbox fetal ECG database show that significant performance improvements, in terms of compression rate and reconstruction quality, can be obtained by the proposed method compared with the state-of-the-art CS-based methods.