Penalized Likelihood Transmission Image Reconstruction:Unconstrained Monotonic Algorithms

Abstract

Statistical reconstruction algorithms in transmission tomography yield improved images relative to the conventional FBP method. The most popular iterative algorithms for this problem are the conjugate gradient (CG) method and ordered subsets (OS) methods. Neither method is ideal. OS methods "converge" quickly, but are suboptimal for problems with factored system matrices. Nonnegativity constraints are not imposed easily by the CG method. To speed convergence, we propose to abandon the nonnegativity constraints (letting the regularization discourage the negative values), and to use quadratic surrogates to choose the step size rather than using an expensive line search. To ensure monotonicity, we develop a modification of the transmission log-likelihood. The resulting algorithm is suitable for large-scale problems with factored system matrices such as X-ray CT image reconstruction with afterglow models. Preliminary results show that the regularization ensures minimal negative values, and that the algorithm is indeed monotone.