Accelerated deterministic annealing algorithms for transmission CT reconstruction using ordered subsets

An approach to the maximum a posteriori (MAP) estimation of attenuation coefficients in transmission tomography is presented. The prior distribution used in our algorithm is based on the line-process model, which has an ability to signal the presence of discontinuities in reconstructed images. This model is particularly applicable to transmission tomography for chest slices, where the anatomical regions are significantly different in their attenuation. To optimize our nonconvex objective function, we use our previously developed deterministic annealing (DA) algorithm, which offers an efficient means of handling nonconvex objectives. To accelerate the convergence speed, we apply the ordered subsets (OS) principle, which processes the data in subsets within each iteration, to the DA algorithm. Our simulation results show that, as the number of subsets increases, the OS procedure applied to our DA algorithm accelerates convergence by a factor proportional to the number of subsets in the early iterates when compared to the standard DA algorithm. The net conclusion is that, with moderate subsets and properly chosen hyperparameters, the OS-DA algorithm provides good-quality reconstructions as well as a significant acceleration.