Sparse spectral-line estimation for nonuniformly sampled multivariate time series: SPICE, LIKES and MSBL

In this paper we deal with the problem of spectral-line analysis of nonuniformly sampled multivariate time series for which we introduce two methods: the first method named SPICE (sparse iterative covariance based estimation) is based on a covariance fitting framework whereas the second method named LIKES (likelihood-based estimation of sparse parameters) is a maximum likelihood technique. Both methods yield sparse spectral estimates and they do not require the choice of any hyperparameters. We numerically compare the performance of SPICE and LIKES with that of the recently introduced method of multivariate sparse Bayesian learning (MSBL).