Compressive Sensing of Electrocardiogram Signals by Promoting Sparsity on the Second-Order Difference and by Using Dictionary Learning

A new algorithm for the reconstruction of electrocardiogram (ECG) signals and a dictionary learning algorithm for the enhancement of its reconstruction performance for a class of signals are proposed. The signal reconstruction algorithm is based on minimizing the lp pseudo-norm of the second-order difference, called as the lp^2d pseudo-norm, of the signal. The optimization involved is carried out using a sequential conjugate-gradient algorithm. The dictionary learning algorithm uses an iterative procedure wherein a signal reconstruction and a dictionary update steps are repeated until a convergence criterion is satisfied. The signal reconstruction step is implemented by using the proposed signal reconstruction algorithm and the dictionary update step is implemented by using the linear least-squares method. Extensive simulation results demonstrate that the proposed algorithm yields improved reconstruction performance for temporally correlated ECG signals relative to the state-of-the-art lp^1d-regularized least-squares and Bayesian learning based algorithms. Also for a known class of signals, the reconstruction performance of the proposed algorithm can be improved by applying it in conjunction with a dictionary obtained using the proposed dictionary learning algorithm.