Accurate imagery recovery using a multi-observation patch model

A patch-based non-local self-similarity prior underpins many of the current state-of-the-art results in image-recovery problems. The associated methods tend to exploit such priors either heuristically in terms of the correlations between similar patches, or implicitly using hand-crafted models. Both approaches have a limited ability to represent image-specific self-similarity statistics, which limits the accuracy of the results. To address this problem, we propose a novel multi-observation patch model (MOPM) for image recovery. The MOPM enables the recovery of a clean patch from multiple noisy observations by using a linear filtering operation on a specific manifold. More importantly, it can be adaptively learned from the intermediate recovered image with a latent variable-based Bayesian learning approach. Thus, the MOPM obtains better representation of the image-specific internal statistics. In addition, the MOPM is naturally integrated into a half-quadratic splitting framework, in which the MOPM can be constantly refined through iterations and ultimately produce promising results. The experimental results on denoising and compressive sensing demonstrate the effectiveness of the MOPM for image recovery.