Distributed compressive sensing for multichannel ECG signals over learned dictionaries

Compressive sensing (CS) is well known for its robust sparse signal reconstruction ability from a smaller set of linear projections taken over an incoherent basis. For mutually correlated signals, a variant of CS called distributed compressive sensing (DCS) is employed. In this work, DCS is proposed to exploit the underlying correlation structure between different channels of multichannel electrocardiogram (MECG) signals. Pathological and normal over-complete dictionaries are learnt using K-SVD algorithm and are used as a set of basis vectors to sparsely represent different disease classes of MECG signals. All channels are simultaneously reconstructed exploiting the joint sparsity of the MECG signal ensembles in the learned dictionary using simultaneous orthogonal matching pursuit (SOMP) algorithm. DCS is found more effective in case of MECG signals as compared to individual channel CS encoding. The joint reconstruction ability of DCS reduces the number of compressed measurements required for accurate reconstruction without affecting the distortion level. The jointly reconstructed MECG signals are validated using different distortion measures like percentage root mean square difference (PRD), wavelet energy based diagnostic distortion (WEDD), signal to noise ratio (SNR) and compression ratio (CR).