Th. Kohler

3D cone-beam CT reconstruction for circular trajectories

3D reconstruction from 2D projections obtained along a single circular source trajectory is most commonly done using an algorithm due to Feldkamp, Davis and Kress. In this paper we propose an alternative approach based on a cone-beam to parallel-beam rebinning step, a corresponding rebinning step into a rectangular virtual detector plane and a filtered backprojection. This approach yields an improved image quality reflected by a decreased low-intensity drop which is well known for 3D reconstruction from projection data obtained along circular trajectories. At the same time the computational complexity is lower than in Feldkamps original approach. Based on this idea, a hybrid 3D cone-beam reconstruction method is formulated that enlarges the reconstruction volume in its dimension along the rotation axis of the cone-beam CT system. This enlargement is achieved by applying different reconstruction conditions for each voxel. An optimal ratio between the reconstructible and irradiated volume of the scanned object is achieved.

Noise and resolution in images reconstructed with FBP and OSC algorithms for CT

This paper presents a comparison between an analytical and a statistical iterative reconstruction algorithm for computed transmission tomography concerning their noise and resolution performance. The reconstruction of two-dimensional images from simulated fan-beam transmission data is performed with a filtered back-projection (FBP) type reconstruction and an iterative ordered subsets convex (OSC) maximum-likelihood method. A special software phantom, which allows measuring the resolution and noise in a nonambiguous way, is used to simulate transmission tomography scans with different signal-to-noise ratios (SNR). The noise and modulation transfer function is calculated for FBP and OSC reconstruction at several positions, distributed over the field-of-view (FOV). The reconstruction with OSC using different numbers of subsets shows an inverse linear relation to the number of iterations that are necessary to reach a certain resolution and SNR, i.e., increasing the number of subsets by a factor x reduces the number of required iterations by the same factor. The OSC algorithm is able to achieve a nearly homogeneous high resolution over the whole FOV, which is not achieved with FBP. The OSC method achieves a lower level of noise compared with FBP at the same resolution. The reconstruction with OSC can save a factor of up to nine of x-ray dose compared with FBP in the investigated range of noise levels.

Automatic phase determination for retrospectively gated cardiac CT

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.

Artifact analysis of approximate helical cone-beam CT reconstruction algorithms.

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.

Angular weighted hybrid cone-beam CT reconstruction for circular trajectories

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.

Motion compensated iterative reconstruction of a region of interest in cardiac cone-beam CT

A method for motion compensated iterative CT reconstruction of a cardiac region-of-interest is presented. The algorithm is an ordered subset maximum likelihood approach with spherically symmetric basis functions, and it uses an ECG for gating. Since the straightforward application of iterative methods to CT data has the drawback that a field-of-view has to be reconstructed, which covers the complete volume contributing to the absorption, region-of-interest reconstruction is applied here. Despite gating, residual object motion within the reconstructed gating window leads to motion blurring in the reconstructed image. To limit this effect, motion compensation is applied. Hereto, a gated 4D reconstruction at multiple phases is generated for the region-of-interest, and a limited set of vascular landmarks are manually annotated throughout the cardiac phases. A dense motion vector field is obtained from these landmarks by scattered data interpolation. The method is applied to two clinical data sets at strongest motion phases. Comparing the method to standard gated iterative reconstruction results shows that motion compensation strongly improved reconstruction quality.

The frequency split method for helical cone-beam reconstruction

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.

A fast and efficient method for sequential cone-beam tomography.

Sequential cone-beam tomography is a method that uses data of two or more parallel circular trajectories of a cone-beam scanner to reconstruct the object function. We 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 exactly 360° in total as seen along the rotation axis. A fast and efficient approximative reconstruction method for the proposed acquisition is presented which uses data from exactly 360° for every object point. It is based on the Tent-FDK method which was recently developed for single circular cone-beam CT. The measurement geometry does not provide sufficient data for exact reconstruction but it is shown that the proposed reconstruction method provides satisfying image quality for small cone angles.

Evaluation of helical cone-beam CT reconstruction algorithms

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.

Depth normalization in MEG/EEG current density imaging

We analyze the minimum norm solution of the biomagnetic inverse problem. It is shown that the bias of this technique, i.e. the tendency to reconstruct superficial currents, can be reduced by the use of an appropriate weighting, which depends the used norm. The weighting factors are calculated by a singular value decomposition of the lead field matrix for each location and a noise regularization technique. With this weighting, the ability to reconstruct deep sources is maintained over the whole volume of sensitivity. The extend of this volume depends on the measurement setup and the noise level.