Simultaneous blur identification and image restoration using the EM algorithm

Algorithms for the simultaneous identification of the blur and the restoration of a noisy blurred image are presented in this paper. The original image and the additive noise are modeled as zero-mean Gaussian random processes, which are characterized by their covariance matrices. The covariance matrices are unknown parameters. The blurring process is specified by its point spread function, which is also unknown. Maximum likelihood estimation is used to find these unknown parameters. In turn, the EM algorithm is exploited to find the maximum likelihood estimates. In applying the EM algorithm, the original image is chosen to be part of the complete data; its estimate, which represents the restored image, is computed in the E-step of the EM iterations. Explicit iterative expressions are derived for the estimation of relevant parameters. Experiments with simulated and photographically blurred images are shown.