The aim of this thesis is to propose and investigate a GPU-based scalable image reconstruction algorithm for transmission tomography based on a Gaussian noise model for the log transformed and calibrated measurements. The proposed algorithm is based on sparse Bayesian learning (SBL) which promotes sparsity of the imaged object by introducing additional latent variables, one for each pixel/voxel, and learning them from the data using an hierarchical Bayesian model.
We address the computational bottleneck of SBL which arises in the computation of posterior variances. Two scalable methods for efficient estimation of variances were studied and tested: the first is based on a matrix probing technique; and the second method is based on a Monte Carlo estimator. Finally, we propose an experimental CT system where instead of using a standard scan around the object, the source locations are selected based on the learned information from previously available measurements, leading to fewer projections.
The keys advantages of the proposed algorithm are: (1) It uses smooth penalties, thus allowing the use of standard gradient-based methods; (2) It does not require any tuning of nuisance parameters; (3) It is highly parallelizable and scalable; (4) It enables adaptive sensing where the measurements are chosen sequentially based on the mutual information measure.
