An efficient algorithm for dempster's completion of block-circulant covariance matrices (IEEE Conference on Decision and Control and European Control Conference)

The present paper deals with maximum entropy completion of partially specified banded block-circulant matrices. This problem has many applications in signal processing since circulants happen to be covariance matrices of stationary periodic processes and maximum entropy completion (i.e. the completion which has maximal determinant) is in fact maximum likelihood estimation subject to conditional independence constraints. Moreover, the maximal determinant completion has the meaning of covariance matrix of stationary reciprocal processes, a class of stochastic processes which extends Markov processes and is particularly useful for modeling signals indexed by space instead of time (think for example of an image). The main contribution of this paper is an efficient algorithm for the solution of this problem.