Fundamentals of digital image processing
Fundamentals of digital image processing
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The EM algorithm is a commonly cited solution in the literature for the problem of maximum likelihood estimation of covariance matrices under a Toeplitz constraint. In this paper, the solution is extended to the case of two-dimensional signals, where spatial stationarity enforces a Toeplitz-block-Toeplitz structure on the covariance matrix.A further generalisation which is presented involves the estimation of the covariance when the observations are subject to subspace interference. It is shown that this situation is amenable to a missing data interpretation, and can be incorporated into the EM iteration with moderate ease. The solution shares all the characteristics of the J-D Toeplitz estimate.The need to solve this problem arises in many invariance applications, where it is required to fit a stationary multivariate normal model to data which is subject to a certain type of interference. The case of unknown DC offset is included in this class.