El-Hadi Djermoune

Sparse multidimensional modal analysis using a multigrid dictionary refinement

We address the problem of multidimensional modal estimation using sparse estimation techniques coupled with an efficient multigrid approach. Modal dictionaries are obtained by discretizing modal functions (damped complex exponentials). To get a good resolution, it is necessary to choose a fine discretization grid resulting in intractable computational problems due to the huge size of the dictionaries. The idea behind the multigrid approach amounts to refine the dictionary over several levels of resolution. The algorithm starts from a coarse grid and adaptively improves the resolution in dependence of the active set provided by sparse approximation methods. The proposed method is quite general in the sense that it allows one to process in the same way mono-and multidimensional signals. We show through simulations that, as compared to high-resolution modal estimation methods, the proposed sparse modal method can greatly enhance the estimation accuracy for noisy signals and shows good robustness with respect to the choice of the number of components.

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 mul-tiresolution. 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.