Penalized likelihood transmission image reconstruction: Unconstrained monotonic algorithms

Statistical reconstruction algorithms in transmission to-mography yield improved images relative to the conven-tional 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 prob-lems with factored system matrices. Nonnegativity con-straints are not imposed easily by the CG method. To speed convergence, we propose to abandon the nonnegativity con-straints (letting the regularization discourage the negative values), and to use application-specic quadratic surrogates to choose the step size rather than using an expensive general-purpose line search. To ensure monotonicity, we develop a modication of the transmission log-likelihood. The re-sulting algorithm is suitable for large-scale problems with factored system matrices such as X-ray CT image recon-struction with afterglow models. Preliminary results show that the regularization ensures minimal negative values, and that the algorithm is indeed monotone. 1