A method for motion compensated iterative CT reconstruction of a cardiac region of interest is presented. The 4D motion field used during reconstruction is obtained from a three-dimensional thin-plate spline warping of a limited number of anatomical point landmarks of the right coronary artery. Results on a clinical case are compared with standard gated iterative reconstruction. The motion compensated iterative reconstruction provides sharp images of the right coronary artery with significantly better image quality compared to traditional gated reconstruction.

This paper presents a framework of non-interactive algorithms for the mapping of blood flow information to vessels in 3D-RA images. With the presented method, mapping of flow information to 3D-RA images is done automatically without user interaction. So far, radiologists had to perform this task by extensive image comparisons and did not obtain visualizations of the results. In our approach, flow information is reconstructed by forward projection of vessel pieces in a 3D-RA image to a two-dimensional projection series capturing the propagation of a short additional contrast agent bolus. For accurate 2D-3D image registration, an efficient patient motion compensation technique is introduced. As an exemplary flow-related quantity, bolus arrival times are reconstructed for the vessel pieces by matching of intensity-time curves. A plausibility check framework was developed which handles projection ambiguities and corrects for noisy flow reconstruction results. It is based on a linear programming approach to model the feeding structure of the vessel. The flow reconstruction method was applied to 12 cases of cerebral stenoses, AVMs and aneurysms, and it proved to be feasible in the clinical environment. The propagation of the injected contrast agent was reconstructed and visualized in three-dimensional images. The flow reconstruction method was able to visualize different types of useful information. In cases of stenosis of the middle cerebral artery (MCA), flow reconstruction can reveal impeded blood flow depending on the severeness of the stenosis. With cases of AVMs, flow reconstruction can clarify the feeding structure. The presented methods handle the problems imposed by clinical demands such as non-interactive algorithms, patient motion compensation, short reconstruction times, and technical requirements such as correction of noisy bolus arrival times and handling of overlapping vessel pieces. Problems occurred mainly in the reconstruction and segmentation of 3D-RA images in cases of complex AVMs. The concentration of injected contrast agent was often not sufficient to provide highly contrasted vessels in 3D-RA images. Another segmentation-related problem is known as 'kissing vessels' [19]. Kissing vessel artifacts introduce artificial vessel junctions and thereby distort the feeding structure of the vessel. This may finally cause implausible flow reconstruction results and inverse flow directions in vessel segments. We are currently planning to validate our reconstruction results using particle imaging velocimetry (PIV). PIV experiments with phantoms, for which the true flow parameters are known, will allow for the assessment of the accuracy of our contrast agent based method. In the context of computational fluid dynamics techniques, the potential of the presented flow reconstruction method is high. Flow reconstruction results based on the presented method could be used both as boundary conditions for simulations and as a reference for the validation of simulation results. Computational fluid dynamics provide useful information such as arterial wall shear stress and complex flow patterns in aneurysms.

In this work, a modification of the well-known algebraic reconstruction technique (ART) is applied to the reconstruction of images based on X-ray transmission measurements. The modified version takes the noise statistics of the measured data into account. The difference between a measured and an estimated line integral that is back-projected during the iteration is weighted by a confidence measure. This measure is inversely proportional to an estimate of the signal-to-noise ratio (SNR) of the line integral. The estimation is done using Gaussian error propagation of the known uncertainty of the measured intensity. The resulting algorithm is as efficient as the original ART and shows significantly better image quality.

A new access scheme for projections in iterative image reconstruction is suggested. It is based on a constant angular increment. The constant is chosen such that the range of 180 degrees is divided by the golden section. It is shown in a simulation study that the method behaves superior to the random access scheme and the scheme based on prime number decomposition.

Katsevich proposed a reconstruction algorithm for helical cone-beam CT which is theoretically exact. Even for large cone angles, it performs very well on static objects. But due to its limitation to the PI illumination window, it produces strong artefacts in the presence of motion. We propose a method to reduce these spreading motion artefacts significantly by adding a correction image. It uses a small portion of the voxel-dependent over-scan. Results of a simulation study with a 128 row scanner are shown.

With the introduction of ultra-fast cone bean scanners, cardiac CT imaging has become feasible. In order to achieve excellent image quality, cardiac phases must be found during which the heart is quasi-stationary. Electrocardiogram (ECG) information does not always correspond to the exact motion-state of the heart, and there is high patient variability with respect to the motion pattern. The clinician has to select stable phases manually without an exact knowledge about the patient-specific motion. Therefore. several high-resolution volumes corresponding to different phases have to be reconstructed. which is an inefficient task. In this contribution, a simple and efficient image-based technique is introduced which is able to deliver patient-specific stable cardiac phases in an automatic fashion. For this purpose, a low-resolution 4D data set is reconstructed in advance. The most stable phases are derived from this 4D data set by calculating the similarity between subsequent positions in the cardiac cycle. Information about the patient-specific motion of the heart can be determined. High-resolution reconstructions are shown at the automatically predicted phase points corresponding to systole and diastole. The images are superior to images reconstructed at other phase points.

Three-dimensional rotational angiography (3D-RA) provides highly accurate images of the morphology of the cerebral vessel tree. In order to enable the reconstruction of blood flow parameters in 3D-RA images, we acquire an additional series of conventional angiograms with high temporal resolution. The propagation of a contrast agent bolus, which is captured by this series, is mapped to the vessel pieces in the 3D-RA image. For each vessel piece, the bolus arrival time is reconstructed by cross-correlation of intensity–time curves. Bolus arrival times may be disturbed due to imperfections of the superposition of 3D and 2D data or noisy image input. This contribution presents a plausibility check framework for noisy bolus arrival times. The framework is based on an individual vessel model that represents the feeding structure of the vessel tree derived from the vessel morphology. Linear programming is used to reconstruct a distribution of bolus arrival times which is in accordance with the vessel model. Flow reconstruction provides useful information for the physician. The visualization of the propagation of contrast agent can be used to assess the hemodynamic relevance of stenoses and clarify the feeding structure of complex arteriovenous malformations (AVMs).

A new approximate method for the utilization of redundant data in helical cone-beam CT is presented. It is based on the observation that the original WEDGE method provides excellent image quality if only little more than 180 degrees data are used for back-projection, and that significant low-frequency artifacts appear if a larger amount of redundant data are used. This degradation is compensated by the frequency split method: The low-frequency part of the image is reconstructed using little more than 180 degrees of data, while the high frequency part is reconstructed using all data. The resulting algorithm shows no cone-beam artifacts in a simulation of a 64-row scanner. It is further shown that the frequency split method hardly degrades the signal-to-noise ratio of the reconstructed images and that it behaves robustly in the presence of motion.

In this study, we apply the algebraic reconstruction technique (ART) to cone-beam CT volume reconstruction. We investigate the effect of various parameters on the spatial resolution of the images: volume grid size, number of iterations, and object size. Simulated data from an analytical phantom function are used to compute the resolution. The results are compared with analytical reconstruction using a cone-beam filtered backprojection algorithm (WEDGE).

3D rotational X-ray imaging is currently most widely applied for the visualization of complex vessel structures and malformations. In addition to the static 3D information, the time-dependent contrast agent wave propagation can be derived using an additional projection series and a corresponding reconstruction. A stabilized flow reconstruction method is presented, which enables the visualization of the contrast agent propagation in 3D. It is based on the framework of linear programming and is a global optimization scheme for a complete vascular tree. A new approach to add a smoothness constraint is presented.

A reconstruction algorithm for helical CT using a 3-Pi acquisition is presented. Here we show, how we can deal with data obtained by an n-Pi acquisition, where n can be any positive odd integer. The method, viz. EnPiT, is a filtered back-projection algorithm and is based on the results obtained for n=1 by A. Katsevich. For an n-Pi acquisition, we have to ensure that all Radon-planes receive the correct weights. Therefore, n different sets of filter-lines are needed. Nevertheless, the presented sets of filter-lines allow for an efficient implementation, such that the computational complexity increases only slowly with n. Simulation results demonstrate that the algorithm works satisfactorily. The reconstructed images exhibit excellent quality

We present an algorithm for helical cone-beam CT, which can detect motion based on the analysis of so-called PI-partners. For each object point, the two independent measurements of the line integral along the PI-line of this object point are considered. It is shown in a simulation study that a difference in these two values correlates well with the occurrence of motion artifacts, if no redundant data are used for the reconstruction. Compared with other projection based motion detection techniques, our approach does not require any rebinning or approximations and it provides a spatially resolved motion estimate and works also in the case of truncated projections. The motion detection method can be readily applied to other complete trajectories like the saddle trajectory.

The recent improvements in CT detector and gantry technology in combination with new heart rate adaptive cone beam reconstruction algorithms enable the visualization of the heart in three dimensions at high spatial resolution. However, the finite temporal resolution still impedes the artifact-free reconstruction of the heart at any arbitrary phase of the cardiac cycle. Cardiac phases must be found during which the heart is quasistationary to obtain outmost image quality. It is challenging to find these phases due to intercycle and patient-to-patient variability. Electrocardiogram (ECG) information does not always represent the heart motion with an adequate accuracy. In this publication, a simple and efficient image-based technique is introduced which is able to deliver stable cardiac phases in an automatic and patient-specific way. From low-resolution four-dimensional data sets, the most stable phases are derived by calculating the object similarity between subsequent phases in the cardiac cycle. Patient-specific information about the object motion can be determined and resolved spatially. This information is used to perform optimized high-resolution reconstructions at phases of little motion. Results based on a simulation study and three real patient data sets are presented. The projection data were generated using a 16-slice cone beam CT system in low-pitch helical mode with parallel ECG recording.

Recently, an exact reconstruction method for helical CT was published by A. Katsevich. The algorithm is of the filtered backprojection type and is, therefore, computationally efficient. Moreover, during backprojection, only data are used which correspond to an illumination interval of 180 degrees as seen from the object-point. We propose a new reconstruction method, which is applicable to data obtained with a 3-Pi acquisition [IEEE Trans. Med. Imaging 19, 848-863 (2000)]. The method uses the same filter types as the Katsevich algorithm, but the directions and the number of the filter lines are chosen differently. For the derivation of the new algorithm, we analyze the relationship of the Katsevich method and radon inversion. A certain radon plane can intersect with the backprojection interval related to a 3-Pi acquisition either once, three, or five times. In analogy to the definition of quasiexactness introduced by Kudo et al. for a 1-Pi acquisition, we use the term quasiexactness for algorithms on a 3-Pi acquisition, if radon planes with one or three intersections within the backprojection interval are treated correctly. Using the results on the relationship with radon inversion, we can prove that our algorithm is quasiexact in this sense. We use simulation results in order to demonstrate that the algorithm yields excellent image quality.

In this work, three different reconstruction algorithms for short scan helical cone-beam CT are compared: Two approximate algorithms, PI-SLANT and WVEDGE-PI, with the recently published exact algorithm by Katsevich. It is shown that WEDGE-PI performs as well as the exact method for a 64 row scanner and almost as well for a 128 row scanner. PI-SLANT produces significantly more artifacts, in particular for the 128 row scanner.

In this paper, four approximate cone-beam CT reconstruction algorithms are compared: Advanced single slice rebinning (ASSR) as a representative of algorithms employing a two dimensional approximation, PI, PI-SLANT, and 3-PI which all use a proper three dimensional back-projection. A detailed analysis of the image artifacts produced by these techniques shows that aliasing in the z-direction is the predominant source of artifacts for a 16-row scanner with 1.25 mm nominal slice thickness. For a detector with isotropic resolution of 0.5 mm, we found that ASSR and PI produce different kinds of artifacts which are almost at the same level, while PI-SLANT produces none of these artifacts. It is shown that the use of redundant data in the 3-PI method suppresses aliasing artifacts efficiently for both scanners.

Hybrid reconstruction techniques have been introduced for the volume reconstruction of axially truncated cone-beam computed tomography projection data acquired along a circular source-detector trajectory. The introduction of weighted half-scan techniques into this framework is described in this paper. Due to the cone-beam geometry it is not possible to perform the weighting on the projections as is typically done in conventional single-line computed tomography. Hence, in this paper we present an efficient way to incorporate angular weighting functions, depending on the object point position, into the framework of hybrid cone-beam reconstruction. Four different angular weighting functions are introduced and discussed with respect to their cone-beam artefact behaviour and their influence on the signal-to-noise ratio. As a result, the most effective angular weighting function for hybrid circular cone-beam reconstruction is determined by means of a simulation study based on mathematical phantoms and clinical data sets. This distance-weighted angular weighting scheme yields the best results in terms of high image quality, low computational complexity and signal-to-noise variations in the reconstruction volume.

Sequential cone-beam tomography is a method where data of two or more circular trajectories are used to reconstruct the object function. The authors propose a condition for the data acquisition that ensures that all object points between two successive circles are irradiated over an angular span of the X-ray source position of 360 degrees in total. A fast and efficient approximative reconstruction method for sequential cone-beam tomography is presented that is based on the tent-FDK method and can handle axially truncated projections.

Forward projection through discrete data sets is a major step in all iterative reconstruction methods. Based on the assumption that the true object function can be described adequately by tri-linear interpolation between the samples, which are located on a cubic grid, the authors propose an efficient and accurate method to calculate line integrals: the line is divided into segments separated by the surfaces of the grid and within each segment the integration is done using Simpson's rule

Reconstructions of generators of biomagnetic and bioelectric activity are nowadays dominated by single or multiple equivalent current dipole models. These methods suffer from the dependence of their results from the Start values of the nonlinear minimization algorithm that optimizes the dipole positions in order to achieve a minimum of the deviation Δ between the measured data M and the forward calculated field distribution L j: Δ2 = ∥ M − L j ∥2. The lead field matrix L depends on the sensor geometry, the dipole positions, and the volume conductor model. The optimum dipole components j that minimize Δ2 can be calculated by j = (L T L)−1 L T M.