Maximum likelihood blur identification and image restoration using the EM algorithm

The authors describe an algorithm for the identification of the blur and the restoration of a noisy blurred image. The original image and the additive noise are modeled as zero-mean Gaussian random processes. Their 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 expectation-maximization (EM) algorithm is exploited in computing the maximum likelihood estimates. In applying the EM algorithm, the original image is part of the complete data; its estimate is computed in the E-step of the EM iterations. Explicit iterative expressions are derived for the estimation. Experimental results on simulated and photographically blurred images are shown