Sparse multigrid modal estimation: Initial grid selection

Modal retrieval problem can be addressed using sparse estimation techniques coupled with a multigrid approach. Selection of the initial grid, in the multigrid algorithm, is a critical problem that needs satisfactory solutions. In this paper we propose a strategy for selecting a coarse initial grid which guarantees convergence of the algorithm even starting with a single atom in the dictionary. The idea is to define the atoms so as their correlation with the signal modes is greater than a specified threshold. We show through simulations that the proposed solution provides accurate estimations even in presence of noise. Moreover, we investigate the convergence of the multigrid algorithm towards the true parameters.