An l0 norm based method for frequency estimation from irregularly sampled data

We present a frequency estimation method based on a sparse representation of irregular samples with an overcomplete basis. We enforce sparsity by imposing penalties based on an approximate ℓ₀- norm. A number of recent theoretical results on compressed sensing justify this choice. Explicitly enforcing the sparsity of the representation is motivated by a desire to obtain a sharp estimate of the frequency spectrum that exhibits super-resolution. Our formulation leads to an optimization problem, which we solve efficiently in an iterative algorithm. The simulation results demonstrate that that the proposed algorithm outperforms several other state-of-art methods.