An efficient algorithm for dempster´s completion of block-circulant covariance matrices

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 ([18], [20], [21]), 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 maximum entropy completion problem for circulant matrices has been solved in [5] and some generalizations are brougth forth in [6]. The main contribution of this paper is an efficient algorithm for its solution.