Covariance estimation for multidimensional data using the EM algorithm

Under a complex-Gaussian data model, a maximum likelihood method based on the iterative expectation-maximization algorithm is given to estimate structured covariance matrices for multidimensional data organized into column-vector form. The covariance structures of interest involve a hierarchy of subblocks within the covariance matrix, and include block-circulant and block Toeplitz matrices and their generalizations. These covariance matrices are elements of certain covariance constraint sets such that each element may be described as a matrix multiplication of a known matrix of Kronecker products and a nonnegative-definite, block-diagonal matrix. Several convergence properties of the estimation procedure are discussed, and an example of algorithm behavior is provided