This paper addresses the problem of estimating the spatial covariance matrix of acoustic sources. This approach improves the localization of correlated sources. Since it provides information on their correlation, it also brings a better characterization of their nature. Two methods are proposed: a penalized approach, with `1 and trace regularization terms, as well as a greedy method (Orthogonal Least Squares), both promoting the sparsity of the coefficients of the matrix and its low rank. Experimental results show the interest of the proposed approaches to locate correlated sources, or in presence of reflections