Stefan Hoppe

A new scheme for view-dependent data differentiation in fan-beam and cone-beam computed tomography

In computed tomography, analytical fan-beam (FB) and cone-beam (CB) image reconstruction often involves a view-dependent data differentiation. The implementation of this differentiation step is critical in terms of resolution and image quality. In this work, we present a new differentiation scheme that is robust to changes in the data acquisition geometry and to coarse view sampling. Our scheme was compared to two previously suggested methods, which we call the direct scheme and the chain-rule scheme. Image reconstructions were performed from computer-simulated data of the Shepp-Logan phantom, the FORBILD thorax phantom and a modified FORBILD head phantom. For FB reconstruction, we investigated three acquisition geometries: a circular, an ellipse-shaped and a square-shaped trajectory. For CB reconstruction, the circle-plus-line trajectory was considered. Image comparison showed that the new scheme performs consistently well when varying the scenario, in both FB and CB geometry, unlike the other two schemes.

Geometric calibration of the circle-plus-arc trajectory

In this paper, a novel geometric calibration method for C-arm cone-beam scanners is presented which allows the calibration of the circle-plus-arc trajectory. The main idea is the separation of the trajectory into two circular segments (circle segment and arc segment) which are calibrated independently. This separation makes it possible to reuse a calibration phantom which has been successfully applied in clinical environments to calibrate numerous routinely used C-arm systems. For each trajectory segment, the phantom is placed in an optimal position. The two calibration results are then combined by computing the transformation the phantom underwent between the independent calibration runs. This combination can be done in a post-processing step by using standard linear algebra. The method is not limited to circle-plus-arc trajectories and works for any calibration procedure in which the phantom has a preferred orientation with respect to a trajectory segment. Results are presented for both simulated as well as real data acquired with a C-arm system. We also present the first image reconstruction results for the circle-plus-arc trajectory using real C-arm data.

Design and implementation of the software architecture for a 3-D reconstruction system in medical imaging

The design and implementation of the reconstruction system in medical X-ray imaging is a challenging issue due to its immense computational demands. In order to ensure an efficient clinical workflow it is inevitable to meet high performance requirements. Hence, the usage of hardware acceleration is mandatory. The software architecture of the reconstruction system is required to be modular in a sense that different accelerator hardware platforms are supported and it must be possible to implement different parts of the algorithm using different acceleration architectures and techniques. This paper introduces and discusses the design of a software architecture for an image reconstruction system that meets the aforementioned requirements. We implemented a multi-threaded software framework that combines two software design patterns: the pipeline and the master/worker pattern. This enables us to take advantage of the parallelism in off-the-shelf accelerator hardware such as multi-core systems, the Cell processor, and graphics accelerators in a very flexible and reusable way.

Cone-beam Tomography from Short-Scan Circle-plus-Arc Data Measured on a C-arm System

In C-arm computed tomography (CT) systems, the source trajectory does not follow an ideal trajectory. Thus, the real data acquisition geometry is typically expressed by a sequence of projection matrices. However, exact reconstruction algorithms are based on an analytic expression of the projection geometry. In this work, we present a reformulation of an exact reconstruction method to handle projection matrices. In particular, the M-line approach is investigated for a short-scan circle-plus-arc data acquisition. The computation of the derivative with respect to the source trajectory is numerically most critical for which a novel and stable implementation is developed. In order to determine the backprojection range, a 2D polygonal weighting scheme is proposed. Image results are presented from phantom data acquired by a Siemens AXIOM Artis C-arm system. Excellent image results are achieved. Due to the complete data acquisition, the problem of cone artifacts is totally resolved.

Truncation correction for oblique filtering lines

State-of-the-art filtered backprojection (FBP) algorithms often define the filtering operation to be performed along oblique filtering lines in the detector. A limited scan field of view leads to the truncation of those filtering lines, which causes artifacts in the final reconstructed volume. In contrast to the case where filtering is performed solely along the detector rows, no methods are available for the case of oblique filtering lines. In this work, the authors present two novel truncation correction methods which effectively handle data truncation in this case. Method 1 (basic approach) handles data truncation in two successive preprocessing steps by applying a hybrid data extrapolation method, which is a combination of a water cylinder extrapolation and a Gaussian extrapolation. It is independent of any specific reconstruction algorithm. Method 2 (kink approach) uses similar concepts for data extrapolation as the basic approach but needs to be integrated into the reconstruction algorithm. Experiments are presented from simulated data of the FORBILD head phantom, acquired along a partial-circle-plus-arc trajectory. The theoretically exact M-line algorithm is used for reconstruction. Although the discussion is focused on theoretically exact algorithms, the proposed truncation correction methods can be applied to any FBP algorithm that exposes oblique filtering lines.

Evaluation of three analytical methods for reconstruction from cone-beam data on a short circular scan

This article focuses on the problem of three- dimensional image reconstruction from cone-beam data acquired along a partial circular scan (short-scan): We present a detailed comparative evaluation of three state-of-the-art analytical algorithms suggested to achieve image reconstruction in this short-scan geometry. Our evaluation involves quantitative studies, such as the estimation of the contrast-to-noise performance, of the achievable spatial resolution and of the cone-beam artifact behavior of these reconstruction algorithms. In addition to that, we also provide a visual assessment of image quality by evaluating reconstructions of the FORBILD head phantom and a disc phantom. The numerical results presented in this paper were obtained using computer-simulated cone-beam data, while focusing on non-truncated projection data and geometry parameters that are similar to those of real medical C-arm devices.

Calibration of the Circle-plus-Arc Trajectory

In this paper, a novel calibration method for C-arm cone-beam (CB) scanners is presented which allows the calibration of the circle-plus-arc trajectory. The circle-plus-arc trajectory has been investigated recently for exact image reconstruction and is especially well suited for C-arm systems. The main idea is the separation of the trajectory into two segments (circle segment and arc segment) which are calibrated independently. For each trajectory segment, a calibration phantom is placed in an optimal way. The calibration results are then combined by computing the transformation the phantom experienced inbetween the independent runs. This combination can be done in a postprocessing step by using the singular value decomposition (SVD). The method works for any calibration procedure in which the phantom has a favored orientation with respect to a trajectory segment. Results are presented for both, simulated as well as real data acquired with a Siemens AXIOM Artis C-arm system.

Resampling density values on R-lines into density values on a Cartesian grid

Three dimensional cone-beam reconstruction methods based on the differentiated backprojection accurately reconstruct objects only along measured lines. Thus, the values on a Cartesian grid need to be interpolated from the known data. The quality of the final reconstruction result depends on the chosen interpolation method. In this work, we discuss three solutions to this interpolation problem, compare them, quantify their resolution property and discuss their computational effort. Two of these solutions are original. Methods are tested on simulated data of the ForBild head and thorax phantoms. Three different source trajectories are investigated: helix, saddle and circle-plus-line. Our results suggest that a carefully chosen interpolation method considerably reduces the computational effort in the reconstruction algorithm while maintaining the image quality.

Cone-Beam Tomography with Linearly Distorted Source Trajectories

A major drawback of Katsevichs exact general cone-beam inversion scheme is the difficulty in finding practical algorithms adapted to every novel type of source trajectory. We succeeded to overcome this problem, and can formulate reconstruction algorithms, for trajectories that are related through a linear distortion to an already studied scenario. The introduced theory yields two reconstruction strategies that are in principle independent from the underlying reconstruction algorithm and are either based on data pre- and post-processing or on adjustment of filtering directions. Numerical results based on simulated cone-beam data are presented.

Accurate image reconstruction using real C-arm data from a Circle-plus-arc trajectory

ObjectiveDeveloping an efficient tool for accurate three-dimensional imaging from projections measured with C-arm systems.Material and methodsA circle-plus-arc trajectory, which is complete and thus amenable to accurate reconstruction, is used. This trajectory is particularly attractive as its implementation does not require moving the patient. For reconstruction, we use the “M-line method”, which allows processing the data in the efficient filtered backprojection mode. This method also offers the advantage of not requiring an ideal data acquisition geometry, i.e., the M-line algorithm can account for known deviations in the scanning geometry, which is important given that sizeable deviations are generally encountered in C-arm imaging.ResultsA robust implementation scheme of the “M-line method” that applies straightforwardly to real C-arm data is presented. In particular, a numerically stable technique to compute the view-dependent derivative with respect to the source trajectory parameter is applied, and an efficient way to compute the π-line backprojection intervals via a polygonal weighting mask is presented. Projection data of an anthropomorphic thorax phantom were acquired on a medical C-arm scanner and used to demonstrate the benefit of using a complete data acquisition geometry with an accurate reconstruction algorithm versus using a state-of-the-art implementation of the conventional Feldkamp algorithm with a circular short scan of cone-beam data. A significant image quality improvement based on visual assessment is shown in terms of cone-beam artifacts.