Matching Pursuit Covariance Learning

In the Multiple Measurements Vector (MMV) model, measurement vectors are connected to unknown, jointly sparse signal vectors through a linear regression model employing a single known measurement matrix (or dictionary). Typically, the number of atoms (columns of the dictionary) is greater than the number measurements and the sparse signal recovery problem is generally ill-posed. In this paper, we treat the signals and measurement noise as independent Gaussian random vectors with unknown signal covariance matrix and noise variance, respectively. Based on the negative log-likelihood function and maximum likelihood principle, we then introduce a matching pursuit covariance learning (CL) algorithm, analogous to popular orthogonal matching pursuit (OMP). Our numerical examples demonstrate effectiveness of the proposed CL strategy in sparse signal recovery where it performs favourably compared to the state-of-the-art algorithms under a broad variety of settings.