Optimal sparse representation algorithms for harmonic retrieval

Abstract

Atomic decomposition is an alternative method for frequency detection in harmonic signals. This type of method produces very concentrated solutions with few nonzero components. It can be used as an alternative to traditional approaches such as principal components frequency estimation methods. We consider methods that find the representation coefficients of a harmonic signal by minimizing the l/sub 1/ norm. For the l/sub 1/ minimization, we compare two interior-point methods to solve the linear program when the basis pursuit principle is implemented. The primal-dual method, which consists of the perturbed optimality conditions of the linear program, proves to be more robust than using the primal method associated with the logarithmic barrier formulation of the linear program. We also contrast the solutions obtained using the Newton interior-point methods with the solution of an iterative reweighted algorithm, which is an efficient alternative method to find a maximally sparse representation.