Advances in single frame image recovery

This thesis tackles a problem of recovering a high resolution image from a single compressed frame. A new image-prior that is devised based on Pearson type VII density is integrated with a Markov Random Field model which has desirable robustness properties. A fully automated hyper-parameter estimation procedure for this approach is developed, which makes it advantageous in comparison with alternatives. Although this recovery algorithm is very simple to implement, it achieves statistically significant improvements over previous results in under-determined problem settings, and it is able to recover images that contain texture. This advancement opens up the opportunities for several potential extensions, of which we pursue two: (i) Most of previous work does not consider any specific extra information to recover the signal. Thus, this thesis exploits the similarity between the signal of interest and a consecutive motionless frame to address this problem. Additional information of similarity that is available is incorporated into a probabilistic image-prior based on the Pearson type VII Markov Random Field model. Results on both synthetic and real data of Magnetic Resonance Imaging (MRI) images demonstrate the effectiveness of our method in both compressed setting and classical super-resolution experiments. (ii) This thesis also presents a multi-task approach for signal recovery by sharing higher-level hyperparameters which do not relate directly to the actual content of the signals of interest but only to their statistical characteristics. Our approach leads to a very simple model and algorithm that can be used to simultaneously recover multipl