Motion-compensated Image Reconstruction with Alternating Minimization

Cardiac computed tomography (CT) is important for its use in diagnosing heart disease. Motion artifacts are a significant issue for cardiac CT image reconstruction. Motioncompensated image reconstruction (MCIR) has the potential to overcome the drawbacks of conventional gated reconstruction methods by exploiting all the measurement data and using motion information. However, MCIR methods are computationally expensive: the system matrix has both the forward-projector and the warp matrices that make it hard to precondition or to apply block iterative algorithms such as ordered-subsets (OS). In this study, we propose a novel approach to solve the image reconstruction part of the MCIR method more efficiently. We use a variable-splitting technique to dissociate the original problem into a number of simpler problems. The proposed method is amenable to preconditioning, parallelization, and application of block iterative algorithms to sub-problems. We demonstrated through a phantom simulation that with simple diagonal or circulant preconditioners, the proposed method shows good convergence rate compared to conjugate gradient (CG) method.