Compressive parameter estimation with multiple measurement vectors via structured low-rank covariance estimation

In this paper, we study the problem of frequency estimation from partial observations of multiple measurement vectors under a sparsity constraint. We develop a two-step approach which first estimates a low-rank Hermitian Toeplitz covariance matrix from the partially observed sample covariance matrix via convex optimization, then recovers the set of frequencies via conventional spectrum estimation methods such as MUSIC. Our method doesn´t assume discretization of the underlying frequencies, therefore overcomes the basis mismatch problem in conventional compressed sensing [1], and can possibly recover a higher number of frequencies than the number of samples per measurement vector. Numerical examples are provided to validate the performance of the proposed algorithm, with comparisons against several existing approaches.