Iterative linear minimum mean-square-error image restoration from partially known blur

We address the problem of space-invariant image restoration when the blurring operator is not known exactly, a situation that arises regularly in practice. To account for this uncertainty, we model the point-spread function as the sum of a known deterministic component and an unknown random one. Such an approach has been studied before, but the problem of estimating the parameters of the restoration filter to our knowledge has not been addressed systematically. We propose an approach based on a Gaussian statistical assumption and derive an iterative, expectation-maximization algorithm that simultaneously restores the image and estimates the required filter parameters. We obtain two versions of the algorithm based on two different models for the statistics of the image. The computations are performed in the discrete Fourier transform domain; thus they are computationally efficient even for large images. We examine the convergence properties of the resulting estimators and evaluate their performance experimentally.