High-accuracy reconstruction of periodic signals based on compressive sensing

The successful deployment of wireless smart transducers in monitoring and control applications is conditioned by their limited power budget. However, the high impact of sampling rate on the overall power consumption of systems dealing with sparse signals can be reduced by introducing a low rate random sampling scheme based on compressive sensing. Although the reconstruction of frequency-sparse signals is a widely studied problem and solutions based on greedy and relaxation methods exist, their performance is degraded in presence of spectral leakage, which affects the sparsity of the signal representation and consequently, its estimation accuracy. In this paper a two-stage optimization approach, called Opti2, is proposed for the reconstruction of periodic signals that can be expressed in terms of fundamental frequency and harmonics. In the first stage, the estimation provided by one of the well-known sparse optimization algorithms is found and used as input to the second stage, where a constrained non-linear optimization problem is solved iteratively. The evaluation of the proposed method demonstrates that it outperforms existing approaches in terms of accuracy, showing its robustness to noise and compression rate.