Hierarchical Bayesian image restoration from partially known blurs

In this paper, we examine the restoration problem when the point-spread fun ction (PSF) of the degradation system is partially known. For this problem, the PSF is assumed to be the sum of a known deterministic and an unknown r andom component. This problem has been examined before; however, in most pr evious works the problem of estimating the parameters that define the resto ration filters was not addressed. fn this paper, two iterative algorithms t hat simultaneously restore the image and estimate the parameters of the res toration filter are proposed using evidence analysis (EA) within the hierar chical Bayesian framework, We show that the restoration step of the first o f these algorithms is in effect almost identical to the regularized constra ined total least-squares (RCTLS) filter, while the restoration step of the second is identical to the linear minimum mean square-error (LMMSE) filter for this problem. Therefore, in this paper we provide a solution to the par ameter estimation problem of the RCTLS filter. We further provide an altern ative approach to the expectation-maximization (EM) framework to derive a p arameter estimation algorithm for the LMMSE filter. These iterative algorit hms are derived in the discrete Fourier transform (DFT) domain; therefore, they are computationally efficient even for large images, Numerical experim ents are presented that test and compare the proposed algorithms.