Implicit Gibbs prior models for tomographic reconstruction

Bayesian model-based inversion has been applied to many applications, such as tomographic reconstructions. However, one limitation of these methods is that prior models are quite simple; so they are not capable of being trained to statistically represent subtle detail in images. In this paper, we demonstrate how novel prior modeling methods based on implicit Gibbs distributions can be used in MAP tomographic reconstruction to improve reconstructed image quality. The concept of the implicit Gibbs distribution is to model the image using the conditional distribution of each pixel given its neighbors and to construct a local approximation of the true Gibbs energy from the conditional distribution. Since the conditional distribution can be trained on a specific dataset, it is possible to obtain more precise and expressive models of images which capture unique structures. In practice, this results in a spatially adaptive MRF model, but it also provides a framework that assures convergence. We present results comparing the proposed method with both state-of-the-art MRF prior models and K-SVD dictionary-based methods for tomographic reconstruction of images. Simulation results indicate that the proposed method can achieve higher resolution recovery.