Alternating Dual Updates Algorithm for X-ray CT Reconstruction on the GPU

Model-based image reconstruction (MBIR) for X-ray computed tomography (CT) offers improved image quality and potential low-dose operation, but has yet to reach ubiquity in the clinic. MBIR methods form an image by solving a large statistically motivated optimization problem, and the long time it takes to numerically solve this problem has hampered MBIR's adoption. We present a new optimization algorithm for X-ray CT MBIR based on duality and group coordinate ascent that may converge even with approximate updates and can handle a wide range of regularizers, including total variation (TV). The algorithm iteratively updates groups of dual variables corresponding to terms in the cost function; these updates are highly parallel and map well onto the GPU. Although the algorithm stores a large number of variables, the "working size" for each of the algorithm's steps is small and can be efficiently streamed to the GPU while other calculations are being performed. The proposed algorithm converges rapidly on both real and simulated data and shows promising parallelization over multiple devices.