Optimization model based sub-nyquist sampling of pulses with various shapes and its application to ECG signals

Recently developed variable pulse width finite rate of innovation (VPW-FRI) theory offers an efficient way for sampling pulse streams with various shapes at the sub-Nyquist rate. Unfortunately, for real signals, noise, and model mismatch will induce inaccuracies to such scheme in the reconstruction process. In this paper, an optimization model-based sub-Nyquist sampling system for pulses with various shapes is proposed, which improves the performance of VPW-FRI scheme under noise and model mismatch situation. Since the real pulse streams with various shapes may be modeled as the sum of an unknown number of Lorentzian pulses and a model mismatch error signal, we build an optimization object function with the purpose of minimizing the energy of this model mismatch error signal. Then, for solving such function, we propose a two-channel sub-Nyquist sampling system to obtain a Fourier coefficients subset and several discrete samples from the input signal. We demonstrate that the best number of Lorentzian pulses and the corresponding pulse parameters can be found by using an improved particle swarm optimization algorithm. Finally, simulations with the electrocardiogram signals in MIT-BIH database have shown that the proposed method has better performance and stability than traditional VPW-FRI scheme.