Sequential image recovery using joint hierarchical Bayesian learning

Abstract: Recovering temporal image sequences (videos) based on indirect, noisy, or incomplete data is an essential yet challenging task. We specifically consider the case where each data set is missing vital information, which prevents the accurate recovery of the individual images. Although some recent (variational) methods have demonstrated high-resolution image recovery based on jointly recovering sequential images, there remain robustness issues due to parameter tuning and restrictions on the type of the sequential images. Here, we present a method based on hierarchical Bayesian learning for the joint recovery of sequential images that incorporates prior intra- and inter-image information. Our method restores the missing information in each image by "borrowing" it from the other images. As a result, \emph{all} of the individual reconstructions yield improved accuracy. Our method can be used for various data acquisitions and allows for uncertainty quantification. Some preliminary results indicate its potential use for sequential deblurring and magnetic resonance imaging.