Sinusoid Signal Estimation using Generalized Block Orthogonal Matching Pursuit Algorithm

We consider general block sparse vectors, which consist of non-zero blocks placed at arbitrary non-overlapping locations and the block partitioning information is unavailable apriori. We propose a generalized block orthogonal matching pursuit (G-BOMP) algorithm to recover the general block sparse vectors, from a set of noisy compressive measurements. We then establish that the sinusoidal signal estimation problem can be solved using the G-BOMP algorithm, by exploiting the structure of spectral leakage in the Fourier domain. We study the performance of the G-BOMP algorithm via simulations and compare it with other algorithms such as OMP, BOMP, newtonized OMP (N-OMP) and spectral compressive sensing (SCS). We observe that our G-BOMP algorithm outperforms OMP, BOMP and SCS methods and is comparable to N-OMP with much lower computational complexity.