Consistency Conditions for Artifact Reduction in Cone-beam CT
Nuclear Medicine, Radiotherapy, Radiobiology
Final Report Abstract
Most artifact reduction methods in flat-panel detector computed tomography (FDCT) rely either on heuristics, prior information additional sensors or iterative procedures. An entire family of artifact reduction methods has found only little application in current FDCT systems. It is known that data consistency conditions describe mathematical redundancies in the projection data which go back to the fact that each projection is composed of line integrals passing through the same object, merely from different directions. These assumption are violated, e.g. by a limited fieldof-view or due to motion of the object during the acquisition. It was demonstrated that data consistency conditions can be used to recover some of that information. The majority of the presented research, however, operates on ideal, often noise free phantom simulations and lacks application to data acquired from real systems because of strong mathematical assumptions. The goal of this project is to extend existing data consistency conditions, which can be practically used for flat-panel detector computed tomography (FDCT) to remedy intrinsic weaknesses of FDCT imaging, most importantly motion and truncation. Our goal is the practical applicability on real data. The project was comprised of three parts, (A) theoretical investigation, (B) numerical implementation and (C) empirical evaluation. Theoretical contributions in work package A are focused on relationships between consistency conditions (A1) and projective geometry as a basis for a common framework (A2). A common framework has been achieved only for epipolar consistency (EC), at this point. Here, we have shown the relationship to well-known fan-beam consistency conditions (FBCC), which in turn can be derived directly from John’s equation. Using stereo rectification, we are able to project any two X-ray images acquired on an FDCT scanner to a situation where FBCC can be applied. We are also able to compute two kinds of epipolar consistency conditions which use Radon intermediate functions, based on Grangeat (GC) and Smith (SC) consistency. All three types, FBCC, GC and SC are types of epipolar consistency, since they share a common underlying geometry. We were able to establish that FBCC and Grangeat consistency are in fact directly related by a derivative in an angular variable. However, evaluation of Grangeat consistency is less computationally demanding. SC replaces the derivative in GC by a ramp filter. SC seems to have entirely different qualities especially with respect to truncation, since the ramp filter is not a local filter. The second part of the project was dedicated specifically to implementation for use with FDCT data. EC remains the most promising approach for general applicability and in work package (B1) we implemented all three kinds of epipolar consistency on the GPU and the source code was made publicly available. While (B1) focuses on the efficient implementation of EC to allow for motion estimation even in large CT data sets, work package (B2) builds an optimization framework around the cost function. The motion model may apply globally to all projections (e.g. detector misalignment for turn-table based computed tomography) or individually to each projection (e.g. 1D heart and respiratory signal extraction from rotational angiography, 2D jitter correction in CT or 3D motion compensation in CT or tomosynthesis), as well as to groups of projections relative to one-another (tracking in fluoroscopy relative to a set of reference projections or raw-data domain 3D-3D registration of CT data sets). All of these have been implemented. Other applications are scatter and beam-hardering correction. The third part of the project was dedicated to validation and evaluation of the new methods. In (C1), we used numerical simulations to show feasibility of tracking in fluoroscopic data, and then acquired a pumpkin phantom on a real scanner to show practical applicability. There is, however, currently no clinical application of the fluoroscopy tracking method. For 3D-3D registration, we conducted both numerical simulation studies and acquired a human head phantom in three positions to test feasibility on a real scanner. Both of these experiments showed promising results. The 3D-3D registration approach can also be used to find 3D symmetry planes in the 2D projection data. Finally, the motion estimation of the thorax was conducted on both numerical simulation and real patient data. The rather simple motion model we assumed does not currently lead to clinically sufficient 3D reconstructions of the vessel tree, however, gating information was successfully and reliably extracted. In work item (C2), planning of the project deviates slightly from our actual work. Originally, it was planned to use data extrapolation methods for limited field-of-view imaging. We investigated one such method based on HLCC. For EC, however, we presented the aforementioned image-processing based approach to de-truncation of limited fieldof-view data based on in-painting, instead of perusing data extrapolation. Implementation and validation of the latter is the enabling work for consistency based motion estimation in rotational angiography. We also attempted to use consistency to improve vessel segmentation. Despite in principle feasible, the methods need further performance boosts to justify their application.
Publications
- Epipolar consistency in transmission imaging. IEEE Transaction on Medical Imaging, 34(11):2205–2219, 2015
André Aichert, Martin Berger, Jian Wang, Nicole Maass, Arnd Doerfler, Joachim Hornegger, and Andreas K. Maier
(See online at https://doi.org/10.1109/TMI.2015.2426417) - Efficient epipolar consistency. In 4th International Conference on Image Formation in X-Ray Computed Tomography, pages 383–386, 2016
André Aichert, Katharina Breininger, Thomas Köhler, and Andreas K. Maier
- An improved extrapolation scheme for truncated ct data using 2d fourier-based helgason-ludwig consistency conditions. International journal of biomedical imaging, 2017
Yan Xia, Martin Berger, Sebastian Bauer, Shiyang Hu, André Aichert, and Andreas K. Maier
(See online at https://doi.org/10.1155/2017/1867025) - Consistencybased respiratory motion estimation in rotational angiography. Medical Physics, 44(9), 2017
Mathias Unberath, André Aichert, Stephan Achenbach, and Andreas K. Maier
(See online at https://doi.org/10.1002/mp.12021) - Motion compensation for cone-beam ct using fourier consistency conditions. Physics in Medicine & Biology, 62(17):7181, 2017
Martin Berger, Yan Xia, Wolfgang Aichinger, Katrin Mentl, Mathias Unberath, André Aichert, Christian Riess, Joachim Hornegger, Rebecca Fahrig, and Andreas K. Maier
(See online at https://doi.org/10.1088/1361-6560/aa8129) - Projective invariants for geometric calibration in flat panel computed tomography. In 5th International Conference on Image Formation in X-Ray Computed Tomography, pages 69–72, 2018
André Aichert, Bastian Bier, Leonhard Rist, and Andreas K. Maier
- Stereo rectification for x-ray data consistency conditions. In 5th International Conference on Image Formation in X-Ray Computed Tomography, pages 198–201, 2018
André Aichert, Jérôme Lesaint, Tobias Würfl, Rolf Clackdoyle, Laurent Desbat, and Andreas K. Maier
