Structured Model Selection for Recovery of Sparse Representations in Nested Periodic Dictionaries

Pouria Saidi, George K. Atia

Abstract: Periodic signals were shown to admit sparse representations in Nested periodic dictionaries (NPDs). Therefore, sparse recovery frameworks have been employed to estimate the periodicity in signals by finding their sparse representations in such dictionaries. However, existing sparse recovery algorithms such as Orthogonal Matching Pursuit (OMP) are oblivious to the structure of the dictionary, and as a result their performance degrade in settings involving periodic mixtures. In this work, we propose new algorithms for structured model selection, termed nested periodic subspace OMP and nested periodic subspace regularized OMP, that leverage the well-known Euler structure and LCM property of NPDs. We evaluate the performance of these methods using both synthesized and real data and show that they can yield better performance than generic recovery algorithms while also saving in computation time.