Nonlinear, noniterative Bayesian tomographic image reconstruction

Abstract

In this research, rather than developing a forward model to be inverted, we propose directly modeling the inverse operator. The goal is to develop a non-iterative Bayesian reconstruction method which requires computation comparable to conventional FBP methods, but achieves quality competitive with that of iterative Bayesian methods such as maximum a posteriori probability (MAP). The method we propose, which we call nonlinear back projection (NBP), forms a back projected image cross-section by applying nonlinear filters to the projected data. This method attempts to directly model a type of optimal inverse operator through off-line training of the non-linear filters using example training data of known image cross sections and noisy realizations of projections. The Radon domain filtering is two-dimensional, exploiting redundancy among adjacent angles' measurements. This direct approach to modeling the inverse operator has several potential advantages which make it interesting. First, the elimination of iterative estimation should save computation time relative to common Bayesian techniques. Secondly, some of the inherently nonlinear attributes of the forward process may be implicitly incorporated into the training of the nonlinear backprojection. Finally, training based on sample images and projections may more effectively incorporate greater complexity in the statistical behavior of images than the simple Markov random field models found in most Bayesian formulations.