Article history: This paper deals with maximum entropy completion of partially specified block-circulant matrices. Since positive definite symmet- ric circulants happen to be covariance matrices of stationary peri- odic processes, in particular of stationary reciprocal processes, this problem has applications in signal processing, in particular to im- age modeling. In fact it is strictly related to maximum likelihood estimation of bilateral AR-type representations of acausal signals subject to certain conditional independence constraints. The maxi- mum entropy completion problem for block-circulant matrices has recently been solved by the authors, although leaving open the problem of an efficient computation of the solution. In this pa- per, we provide an efficient algorithm for computing its solution which compares very favorably with existing algorithms designed for positive definite matrix extension problems. The proposed al- gorithm benefits from the analysis of the relationship between our problem and the band-extension problem for block-Toeplitz matri- ces also developed in this paper.
['Francesca P. Carli', 'Augusto Ferrante', 'Michele Pavon', 'Giorgio Picci']
An efficient algorithm for maximum entropy extension of block-circulant covariance matrices