Adaptive wavelet graph model for Bayesian tomographic reconstruction

We introduce an adaptive wavelet graph image model applicable to Bayesian tomographic reconstruction and other problems with nonlocal observations. The proposed model captures coarse-to-fine scale dependencies in the wavelet tree by modeling the conditional distribution of wavelet coefficients given overlapping windows of scaling coefficients containing coarse scale information. This results in a graph dependency structure which is more general than a quadtree, enabling the model to produce smooth estimates even for simple wavelet bases such as the Haar basis. The inter-scale dependencies of the wavelet graph model are specified using a spatially nonhomogeneous Gaussian distribution with parameters at each scale and location. The parameters of this distribution are selected adaptively using nonlinear classification of coarse scale data. The nonlinear adaptation mechanism is based on a set of training images. In conjunction with the wavelet graph model, we present a computationally efficient multiresolution image reconstruction algorithm. This algorithm is based on iterative Bayesian space domain optimization using scale recursive updates of the wavelet graph prior model. In contrast to performing the optimization over the wavelet coefficients, the space domain formulation facilitates enforcement of pixel positivity constraints. Results indicate that the proposed framework can improve reconstruction quality over fixed resolution Bayesian methods.