Adaptive refinement in maximally sparse harmonic signal retrieval

In this paper, we investigate improvements to the iterative re-weighted method of best basis selection for the problem of harmonic retrieval. We describe a computationally efficient (adaptive) refinement of the frequency scale to improve resolution by strategically increasing the dictionary of basis vectors. We also assess the efficacy of using a priori information regarding the number of sinusoidal components, to choose the regularization parameter in the noisy data problem. Computer simulations are used to assess the behavior of various schemes and the following combined approach is suggested: perform adaptive refinement without regularization first before incorporating the regularization.