Iterative procedure for estimating frequency components of a polyharmonic signal

Computing sparse approximation of a signal is a demanding task encountered by such processing techniques as compressed sensing. Estimation of the frequencies of a sum of sinusoidal signals with unknown amplitudes and phases in the presence of noise by means of nonlinear least squares allows to achieve high resolution between close frequencies while keeping the estimation error low. However, computing that estimate incurs significant computational expenses due to the presence of multiple local minima in the object function. This article presents an algorithm that allows finding the estimates without resorting to global multidimensional search.