Opti2: A reconstruction approach for periodic signals using compressive sensing

The reconstruction of frequency-sparse signals from a low number of samples using a compressed sensing concept is a widely studied problem and solutions based on greedy and relaxation methods are available. However, 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. The estimation provided by basis pursuit denoising (BPDN) sparse optimization approach is computed in the first stage and used as initial guess for the second stage, where a constrained non-linear optimization problem is solved in an iterative fashion, aiming to improve the estimation of the signal parameters. The evaluation of the proposed method with simulated and experimental data demonstrates that it outperforms existing approaches in term of accuracy, showing its robustness to noise, compression rate and dictionary refinement factor.