Parallelizable Bayesian tomography algorithms with rapid, guaranteed convergence

Bayesian tomographic reconstruction algorithms generally require the effici ent optimization of a functional of many variables, In this setting, as wel l as in many other optimization tasks, functional substitution (FS) has bee n widely applied to simplify each step of the iterative process. The functi on to be minimized is replaced locally by an approximation having a more ea sily manipulated form, e.g., quadratic, but which maintains sufficient simi larity to descend the true functional while computing only the substitute. In this paper, we provide two new applications of FS methods in iterative c oordinate descent for Bayesian tomography, The first is a modification of o ur coordinate descent algorithm with one-dimensional (1-D) Newton-Raphson a pproximations to an alternative quadratic which allows convergence to be pr oven easily. In simulations, we fmd essentially no difference in convergenc e speed between the two techniques. We also present a new algorithm which e xploits the FS method to allow parallel updates of arbitrary sets of pixels using computations similar to iterative coordinate descent. The theoretica l potential speed up of parallel implementations is nearly linear with the number of processors if communication costs are neglected.