Abstract-Respiratory motion is a major concern in cone-beam (CB) computed tomography (CT) of the thorax. It causes artifacts such as blur, streaks, and bands, in particular when using slow-rotating scanners mounted on the gantry of linear accelerators. In this paper, we compare two approaches for motion-compensated CBCT reconstruction of the thorax. The first one is analytic; it is heuristically adapted from the method of Feldkamp, Davis, and Kress (FDK). The second one is algebraic: the system of linear equations is generated using a new algorithm for the projection of deformable volumes and solved using the Simultaneous Algebraic Reconstruction Technique (SART). For both methods, we propose to estimate the motion on patient data using a previously acquired 4-D CT image. The methods were tested on two digital and one mechanical motion-controlled phantoms and on a patient dataset. Our results indicate that the two methods correct most motion artifacts. However, the analytic method does not fully correct streaks and bands even if the motion is perfectly estimated due to the underlying approximation. In contrast, the algebraic method allows us full correction of respiratory-induced artifacts.

This work is dedicated to the reduction of reconstruction artefacts due to motion occurring during the acquisition of computerized tomographic projections. This problem has to be solved when imaging moving organs such as the lungs or the heart. The proposed method belongs to the class of motion compensation algorithms, where the model of motion is included in the reconstruction formula. We address two fundamental questions. First what conditions on the deformation are required for the reconstruction of the object from projections acquired sequentially during the deformation, and second how do we reconstruct the object from those projections. Here we answer these questions in the particular case of 2D general time-dependent affine deformations, assuming the motion parameters are known. We treat the problem of admissibility conditions on the deformation in the parallel-beam and fan-beam cases. Then we propose exact reconstruction methods based on rebinning or sequential FBP formulae for each of these geometries and present reconstructed images obtained with the fan-beam algorithm on simulated data.