Hyperparameter estimation in image restoration problems with partially known blurs

This work is motivated by the observation that it is not possible to reliably estimate simultaneously all the necessary hyperparameters in an image restoration problem when the point-spread function is assumed to be the sum of a known deterministic and an unknown random component. To solve this problem we propose to use gamma hyperpriors for the unknown hyperparameters. Two iterative algorithms that simultaneously restore the image and estimate the hyperparameters are derived based on the application of the evidence analysis within the hierarchical Bayesian framework. Numerical experiments are presented that show the benefits of introducing hyperpriors for this problem. Subject terms: Image restoration, partially-known blur, hyperparameter estimation, gamma hyperpriors, Bayesian estimation. 1