Sparse multiresolution modal estimation

Methods for subset selection can be used to address the modal retrieval problem using an overcomplete dictionary composed of elementary damped sinusoids. Apart from the related optimization problems, the major difficulty with such techniques is the size of dictionary allowing one to get a sufficient reconstruction error. In this paper, we propose an efficient computational approach combining sparse approximation and multiresolution. The idea behind multiresolution amounts to refine the dictionary of damped exponentials over several levels of resolution. The algorithm starts from a coarse grid and adaptively improves the resolution as a function of the active set obtained using sparse approximation methods. We show through simulation results that sparse methods coupled to the multiresolution approach can greatly enhance the estimation accuracy for noisy signals.