An accelerated motion-compensated iterative reconstruction technique for dynamic computed tomography

This work presents an efficient technique for simultaneously reconstructing an image of a moving object from X-ray projections along with estimating the motion parameters. Current state-of-the-art iterative methods rely on objective functions that contain the solution of an iterative procedure as one of its terms. This complicates the reconstruction process as it leads to nested iterations and makes analytic differentiation impractical. The presented technique relies on an objective function that simultaneously depends on the image and the motion parameters. The derivatives of this objective function towards the image and the motion parameters are known exactly and implemented matrix free and in parallel. Moreover, the stepsizes of both the iterative reconstruction and motion parameter estimation schemes are chosen following a mathematical formulation that guarantees a fast convergence speed. The result is a method that not only needs less iterations, but also removes the need to tune the finite differences stepsize and the number of inner iterations, which allows for efficient, scalable reconstruction using modern optimizers, without nested iterations.