Simultaneous identification and restoration of images using maximum likelihood estimation
'I'his paper deals with simultaneous identification and restoration of images. By idqitification, we mean the estimation of the parameters characterizing the degradation mechanisms. The original image and the additive noise are assumed to be zeroniean Gaussian random processes. Their autocovariance ma trices arc unknown parameters. Blurring is part of the degradation. It is specified by its point spread function, which is also an unknown parameter to be estimated. Maximum likelihood estimation is used to find those unknown parameters. In turn, the EM algorithm is used to find the maximum likelihood estimates. In applying the EM algorithm, the observed image is treated as the incomplete data, which turns out to be a linear transformation of the complete data. Diffefent choices of complete data are investigated. Under the assumptioil that the image covariance and distortion matrices are circulant, the estimation of the unknown parameters becomes feasible. Explicit iterative expressions are derived for the estimation. The restored image is computed in the E-step of the EM algorithm.