General reconstruction theory for multislice X-ray computed tomography with a gantry tilt

Cone-beam imaging with tilted rotation axis: Method and performance evaluation

PURPOSE

The recently introduced robotic x-ray systems provide the flexibility to acquire cone-beam computed tomography (CBCT) data using customized, application-specific source-detector trajectories. We exploit this capability to mitigate the effects of x-ray scatter and noise in CBCT imaging of weight-bearing foot and cervical spine (C-spine) using scan orbits with a tilted rotation axis.

METHODS

We used an advanced CBCT simulator implementing accurate models of x-ray scatter, primary attenuation, and noise to investigate the effects of the orbital tilt angle in upright foot and C-spine imaging. The system model was parameterized using a laboratory version of a three-dimensional (3D) robotic x-ray system (Multitom RAX, Siemens Healthineers). We considered a generalized tilted axis scan configuration, where the detector remained parallel to patient's long body axis during the acquisition, but the elevation of source and detector was changing. A modified Feldkamp-Davis-Kress (FDK) algorithm was developed for reconstruction in this configuration, which departs from the FDK assumption of a detector that is perpendicular to the scan plane. The simulated foot scans involved source-detector distance (SDD) of 1386 mm, orbital tilt angles ranging 10° to 40°, and 400 views at 1 mAs/view and 0.5° increment; the C-spine scans involved -25° to -45° tilt angles, SDD of 1090 mm, and 202 views at 1.3 mAs and 1° increment The imaging performance was assessed by projection-domain measurements of the scatter-to-primary ratio (SPR) and by reconstruction-domain measurements of contrast, noise and generalized contrast-to-noise ratio (gCNR, accounting for both image noise and background nonuniformity) of the metatarsals (foot imaging) and cervical vertebrae (spine imaging). The effects of scatter correction were also compared for horizontal and tilted scans using an ideal Monte Carlo (MC)-based scatter correction and a frame-by-frame mean scatter correction.

RESULTS

The proposed modified FDK, involving projection resampling, mitigated streak artifacts caused by the misalignment between the filtering direction and the detector rows. For foot imaging (no grids), an optimized 20° tilted orbit reduced the maximum SPR from ~1.5 in a horizontal scan to <0.5. The gCNR of the second metatarsal was enhanced twofold compared to a horizontal orbit. For the C-spine (with vertical grids), imaging with a tilted orbit avoided highly attenuating x-ray paths through the lower cervical vertebrae and shoulders. A -35° tilted orbit yielded improved image quality and visualization of the lower cervical spine: the SPR of lower cervical vertebrae was reduced from ~10 (horizontal orbit) to <6 (tilted orbit), and the gCNR for C5-C7 increased by a factor of 2. Furthermore, tilted orbits showed potential benefits over horizontal orbits by enabling scatter correction with a simple frame-by-frame mean correction without substantial increase in noise-induced artifacts after the correction.

CONCLUSIONS

Tilted scan trajectories, enabled by the emerging robotic x-ray system technology, were optimized for CBCT imaging of foot and cervical spine using an advanced simulation framework. The results demonstrated the potential advantages of tilted axis orbits in mitigation of scatter artifacts and improving contrast-to-noise ratio in CBCT reconstructions.

Simulation tools for two-dimensional experiments in x-ray computed tomography using the FORBILD head phantom

Mathematical phantoms are essential for the development and early stage evaluation of image reconstruction algorithms in x-ray computed tomography (CT). This note offers tools for computer simulations using a two-dimensional (2D) phantom that models the central axial slice through the FORBILD head phantom. Introduced in 1999, in response to a need for a more robust test, the FORBILD head phantom is now seen by many as the gold standard. However, the simple Shepp-Logan phantom is still heavily used by researchers working on 2D image reconstruction. Universal acceptance of the FORBILD head phantom may have been prevented by its significantly higher complexity: software that allows computer simulations with the Shepp-Logan phantom is not readily applicable to the FORBILD head phantom. The tools offered here address this problem. They are designed for use with Matlab®, as well as open-source variants, such as FreeMat and Octave, which are all widely used in both academia and industry. To get started, the interested user can simply copy and paste the codes from this PDF document into Matlab® M-files.

Backprojection-filtration reconstruction without invoking a spatially varying weighting factor

PURPOSE

To develop a backprojection-filtration (BPF) algorithm with improved noise properties over the existing BPF algorithm through utilizing (approximate) redundant information in circular cone-beam or fan-beam scans.

METHODS

The backprojection steps in the existing filtered-backprojection (FBP) and BPF algorithms for fan-beam and cone-beam projections invoke spatially varying weighting factors, which may not only increase the computational load in image reconstruction but also, more importantly, result in reconstruction artifacts. Redundant information in fan-beam projections has been exploited for eliminating the weighting factor in the existing FBP algorithm. However, the new FBP algorithm cannot be applied to image reconstruction in a region of interest from transversely truncated data. In this work, the authors identify approximate data redundancy in circular cone-beam projections and propose a new BPF algorithm in which the approximate data redundancy is exploited for eliminating the spatially varying weighting factor in the existing BPF algorithm.

RESULTS

The authors have implemented and evaluated the proposed BPF algorithm in numerical studies of reconstructing 3D images from both the nontruncated and truncated projection data in a circular cone-beam scan. The results of numerical studies demonstrate that the proposed BPF algorithm retains the resolution property of the existing BPF algorithm, and that it can also reconstruct accurately ROI images from truncated data. More importantly, the results also indicate that the proposed BPF algorithm not only is computationally more efficient but also yields generally lower image variances than the existing BPF algorithm.

CONCLUSIONS

A BPF algorithm was proposed that not only retains the desirable properties of the existing BPF algorithm but also possesses improved computational and noise properties over the latter.

A novel approach to reduce breast radiation exposure with coronary CTA: angled axial image acquisition

RATIONALE AND OBJECTIVES

To determine whether angled gantry acquisition might be used to image the heart with a shorter scan length and reduced breast exposure during coronary computed tomography angiography.

MATERIALS AND METHODS

One hundred consecutive coronary computed tomography angiography examinations of female patients were retrospectively evaluated to define the angle between the long axis of the left heart and the axial imaging plane. The scan length required to image the entire left ventricle along with the coronary arteries was measured for an axial scan plane as well as for a scan plane parallel to the long axis of the left heart. The overlap between these imaging volumes and the lower portion of the breast was measured.

RESULTS

The long axis of the left heart varied from 7 degrees to 54 degrees off the axial plane (mean 32 degrees +/- 7 degrees ). The required scan length to include the entire left ventricle and coronary arteries ranged from 8.2 to 12.4 cm (mean, 10.0 +/- 0.9 cm) for the axial scan plane and 5.6-10.1 cm (mean, 7.5 +/- 0.8 cm) for a scan plane parallel to the long axis of the heart (P < .001). cCTA in the axial plane required a 7.4 +/- 1.6 cm overlap with the lower breast, whereas cCTA in the long axis of the heart reduced the overlap to 4.5 +/- 1.8 cm (P < .001).

CONCLUSIONS

Using an angled gantry approach, the coronary arteries can be fully imaged in a plane along the long axis of the left heart with a single 10-cm acquisition and with substantial reduction in amount of breast tissue within the irradiated field.

Exact image reconstruction for a circle and line trajectory with a gantry tilt

We investigate image reconstruction with a circle and line trajectory with a tilted gantry. We derive new equations for reconstruction from the line data, such as equations of filtering lines, range of filtering lines and range of the line scan. We analyze the detector requirements and show that the line scan does not impose extra requirements on the cylindrical detector size with our algorithm, that is, the axial truncation of the filtering lines does not occur. We discuss full-scan and short-scan versions of the algorithm. Evaluation of our algorithm uses simulated and real 256-slice data.

Gantry tilted Tilted Plane Feldkamp Type Reconstruction Algorithm

An approximate image reconstruction method for gantry tilted multi slice computed tomography (MSCT) is presented in this paper, which extends the Feldkamp cone beam reconstruction algorithm to overcome its inaccuracy problem caused by large cone angle. This is done by tilting the reconstructing planes to minimize the cone angle and optimally fitting the spiral segment of the source. It is shown that the image reconstruction performance of the proposed algorithm is superior to that of the Feldkamp reconstruction algorithm. Because a 3D projection data set is employed, the proposed algorithm can use the projection more efficiently than 2D approximate reconstruction algorithms. With the reduced distance from the X-ray source to the reconstruction plane, the maximum pitch value of the proposed algorithm is larger than that of conventional Feldkamp algorithm. The proposed algorithm can archive higher volume coverage speed than Feldkamp algorithm.

Chord-based image reconstruction in cone-beam CT with a curved detector

Modern computed tomography (CT) scanners use cone-beam configurations for increasing volume coverage, improving x-ray-tube utilization, and yielding isotropic spatial resolution. Recently, there have been significant developments in theory and algorithms for exact image reconstruction from cone-beam projections. In particular, algorithms have been proposed for image reconstruction on chords; and advantages over the existing algorithms offered by the chord-based algorithms include the high flexibility of exact image reconstruction for general scanning trajectories and the capability of exact reconstruction of images within a region of interest from truncated data. These chord-based algorithms have been developed only for flat-panel detectors. Many cone-beam CT scanners employ curved detectors for important practical considerations. Therefore, in this work, we have derived chord-based algorithms for a curved detector so that they can be applied to reconstructing images directly from data acquired by use of a CT scanner with a curved detector. We have also conducted preliminary numerical studies to demonstrate and evaluate the reconstruction properties of the derived chord-based algorithms for curved detectors.

Tilted cone-beam reconstruction with row-wise fan-to-parallel rebinning

Reconstruction algorithms for cone-beam CT have been the focus of many studies. Several exact and approximate reconstruction algorithms were proposed for step-and-shoot and helical scanning trajectories to combat cone-beam related artefacts. In this paper, we present a new closed-form cone-beam reconstruction formula for tilted gantry data acquisition. Although several algorithms were proposed in the past to combat errors induced by the gantry tilt, none of the algorithms addresses the scenario in which the cone-beam geometry is first rebinned to a set of parallel beams prior to the filtered backprojection. We show that the image quality advantages of the rebinned parallel-beam reconstruction are significant, which makes the development of such an algorithm necessary. Because of the rebinning process, the reconstruction algorithm becomes more complex and the amount of iso-centre adjustment depends not only on the projection and tilt angles, but also on the reconstructed pixel location. In this paper, we first demonstrate the advantages of the row-wise fan-to-parallel rebinning and derive a closed-form solution for the reconstruction algorithm for the step-and-shoot and constant-pitch helical scans. The proposed algorithm requires the 'warping' of the reconstruction matrix on a view-by-view basis prior to the backprojection step. We further extend the algorithm to the variable-pitch helical scans in which the patient table travels at non-constant speeds. The algorithm was tested extensively on both the 16- and 64-slice CT scanners. The efficacy of the algorithm is clearly demonstrated by multiple experiments.

A shift-invariant filtered backprojection (FBP) cone-beam reconstruction algorithm for the source trajectory of two concentric circles using an equal weighting scheme

In this paper, a shift-invariant filtered backprojection cone-beam image reconstruction algorithm is derived, based upon Katsevich's general inversion scheme, and validated for the source trajectory of two concentric circles. The source trajectory is complete according to Tuy's data sufficiency condition and is used as the basis for an exact image reconstruction algorithm. The algorithm proceeds according to the following steps. First, differentiate the cone-beam projection data with respect to the detector coordinates and with respect to the source trajectory parameter. The data are then separately filtered along three different orientations in the detector plane with a shift-invariant Hilbert kernel. Eight different filtration groups are obtained via linear combinations of weighted filtered data. Voxel-based backprojection is then carried out from eight sets of view angles, where separate filtered data are backprojected from each set according to the backprojection sets' associated filtration group. The algorithm is first derived for a scanning configuration consisting of two concentric and orthogonal circles. By performing an affine transformation on the image object, the developed image reconstruction algorithm has been generalized to the case where the two concentric circles are not orthogonal. Numerical simulations are presented to validate the reconstruction algorithm and demonstrate the dose advantage of the equal weighting scheme.

An Approximate Cone Beam Reconstruction Algorithm for Gantry-Tilted CT Using Tangential Filtering

FDK algorithm is a well-known 3D (three-dimensional) approximate algorithm for CT (computed tomography) image reconstruction and is also known to suffer from considerable artifacts when the scanning cone angle is large. Recently, it has been improved by performing the ramp filtering along the tangential direction of the X-ray source helix for dealing with the large cone angle problem. In this paper, we present an FDK-type approximate reconstruction algorithm for gantry-tilted CT imaging. The proposed method improves the image reconstruction by filtering the projection data along a proper direction which is determined by CT parameters and gantry-tilted angle. As a result, the proposed algorithm for gantry-tilted CT reconstruction can provide more scanning flexibilities in clinical CT scanning and is efficient in computation. The performance of the proposed algorithm is evaluated with turbell clock phantom and thorax phantom and compared with FDK algorithm and a popular 2D (two-dimensional) approximate algorithm. The results show that the proposed algorithm can achieve better image quality for gantry-tilted CT image reconstruction.

Theory and algorithms for image reconstruction on chords and within regions of interest

We introduce a formula for image reconstruction on a chord of a general source trajectory. We subsequently develop three algorithms for exact image reconstruction on a chord from data acquired with the general trajectory. Interestingly, two of the developed algorithms can accommodate data containing transverse truncations. The widely used helical trajectory and other trajectories discussed in literature can be interpreted as special cases of the general trajectory, and the developed theory and algorithms are thus directly applicable to reconstructing images exactly from data acquired with these trajectories. For instance, chords on a helical trajectory are equivalent to the n-PI-line segments. In this situation, the proposed algorithms become the algorithms that we proposed previously for image reconstruction on PI-line segments. We have performed preliminary numerical studies, which include the study on image reconstruction on chords of two-circle trajectory, which is nonsmooth, and on n-PI lines of a helical trajectory, which is smooth. Quantitative results of these studies verify and demonstrate the proposed theory and algorithms.

Image reconstruction for the circle-and-arc trajectory

Proposed is an exact shift-invariant filtered backprojection algorithm for the circle-and-arc trajectory. The algorithm has several important features. First, it allows for the circle to be incomplete. Second, axial truncation of the cone beam data is allowed. Third, the length of the arc is determined only by the region of interest and is independent of the size of the entire object. The algorithm is quite flexible and can be used for even more general trajectories that consist of several circular segments and arcs. The algorithm applies also in the case when the circle (or, circles) is complete. A numerical experiment with the clock phantom demonstrated good image quality.