Hyperparameter estimation using hyperpriors for hierarchical Bayesian image restoration from partially known blurs

In this paper we examine the problem of estimating the hyperparameters in image restoration when the point-spread function (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 random component. In this paper two iterative algorithms are proposed that simultaneously restor the image and estimate the hyperparameters of the restoration filter using hyperprior. These algorithms are based on evidence analysis within the hierarchical Bayesian framework. This work was motivated by the observation that it is not possible to simultaneously estimate all the necessary hyperparameters for this problem without any prior knowledge about them. More specifically, we observed in our previous work that we cannot estimate accurately at the same time the hyperparameters and thus facilitate this estimation problem. The proposed iterative algorithms can be derived in the discrete Fourier transform domain, therefore, they are computationally efficient even for large images. Numerical experiments are presented where the benefits of introducing hyperpriors are demonstrated.