Circular Source Trajectory Research Articles

Three-Dimensional Weighting in Cone Beam FBP Reconstruction and Its Transformation Over Geometries

With substantially increased number of detector rows in multidetector CT (MDCT), axial scan with projection data acquired along a circular source trajectory has become the method-of-choice in increasing clinical applications. Recognizing the practical relevance of image reconstruction directly from the projection data acquired in the native cone beam (CB) geometry, especially in scenarios wherein the most achievable in-plane resolution is desirable, we present a three-dimensional (3-D) weighted CB-FBP algorithm in such geometry in this paper. We start the algorithm's derivation in the cone-parallel geometry. Via changing of variables, taking the Jacobian into account and making heuristic and empirical assumptions, we arrive at the formulas for 3-D weighted image reconstruction in the native CB geometry. Using the projection data simulated by computer and acquired by an MDCT scanner, we evaluate and verify performance of the proposed algorithm for image reconstruction directly from projection data acquired in the native CB geometry. The preliminary data show that the proposed algorithm performs as well as the 3-D weighted CB-FBP algorithm in the cone-parallel geometry. The proposed algorithm is anticipated to find its utility in extensive clinical and preclinical applications wherein the reconstruction of images in the native CB geometry, i.e., the geometry for data acquisition, is of relevance.

Axial Cone-Beam Reconstruction by Weighted BPF/DBPF and Orthogonal Butterfly Filtering.

The backprojection-filtration (BPF) and the derivative backprojection filtered (DBPF) algorithms, in which Hilbert filtering is the common algorithmic feature, are originally derived for exact helical reconstruction from cone-beam (CB) scan data and axial reconstruction from fan beam data, respectively. These two algorithms can be heuristically extended for image reconstruction from axial CB scan data, but induce severe artifacts in images located away from the central plane, determined by the circular source trajectory. We propose an algorithmic solution herein to eliminate the artifacts. The solution is an integration of three-dimensional (3-D) weighted axial CB-BPF/DBPF algorithm with orthogonal butterfly filtering, namely axial CB-BPF/DBPF cascaded with orthogonal butterfly filtering. Using the computer simulated Forbild head and thoracic phantoms that are rigorous in inspecting the reconstruction accuracy, and an anthropomorphic thoracic phantom with projection data acquired by a CT scanner, we evaluate the performance of the proposed algorithm. Preliminary results show that the orthogonal butterfly filtering can eliminate the severe streak artifacts existing in the images reconstructed by the 3-D weighted axial CB-BPF/DBPF algorithm located at off-central planes. Integrated with orthogonal butterfly filtering, the 3-D weighted CB-BPF/DBPF algorithm can perform at least as well as the 3-D weighted CB-FBP algorithm in image reconstruction from axial CB scan data. The proposed 3-D weighted axial CB-BPF/DBPF cascaded with orthogonal butterfly filtering can be an algorithmic solution for CT imaging in extensive clinical and preclinical applications.

Dedicated breast CT: radiation dose for circle-plus-line trajectory

Dedicated breast CT prototypes used in clinical investigations utilize single circular source trajectory and cone-beam geometry with flat-panel detectors that do not satisfy data-sufficiency conditions and could lead to cone beam artifacts. Hence, this work investigated the glandular dose characteristics of a circle-plus-line trajectory that fulfills data-sufficiency conditions for image reconstruction in dedicated breast CT. Monte Carlo-based computer simulations were performed using the GEANT4 toolkit and was validated with previously reported normalized glandular dose coefficients for one prototype breast CT system. Upon validation, Monte Carlo simulations were performed to determine the normalized glandular dose coefficients as a function of x-ray source position along the line scan. The source-to-axis of rotation distance and the source-to-detector distance were maintained constant at 65 and 100 cm, respectively, in all simulations. The ratio of the normalized glandular dose coefficient at each source position along the line scan to that for the circular scan, defined as relative normalized glandular dose coefficient (RD(g)N), was studied by varying the diameter of the breast at the chest wall, chest-wall to nipple distance, skin thickness, x-ray beam energy, and glandular fraction of the breast. The RD(g)N metric when stated as a function of source position along the line scan, relative to the maximum length of line scan needed for data sufficiency, was found to be minimally dependent on breast diameter, chest-wall to nipple distance, skin thickness, glandular fraction, and x-ray photon energy. This observation facilitates easy estimation of the average glandular dose of the line scan. Polynomial fit equations for computing the RD(g)N and hence the average glandular dose are provided. For a breast CT system that acquires 300-500 projections over 2π for the circular scan, the addition of a line trajectory with equal source spacing and constant x-ray beam quality (kVp and HVL) and mAs matched to the circular scan, will result in less than 0.18% increase in average glandular dose to the breast per projection along the line scan.

Cone‐beam CT image reconstruction with extended range

In circular cone-beam CT the Feldkamp [Feldkamp-Davis-Kress (FDK)] algorithm is the most prominent image reconstruction algorithm. For example, in radiation oncology images reconstructed with the Feldkamp algorithm are used for accurate patient positioning. The scan and reconstruction volumes are limited by the size of the flat panel detector. Flat panel detectors, however, are expensive and difficult to manufacture in large size. For numerous treatment techniques, extending this scan volume would be very beneficial. In most applications, data from 360 degrees or more are available. However, usually only those slices are reconstructed where each pixel is seen under the full 360 degree range. Yet for a 360 degree scan there are regions that are seen by less than 360 degrees, namely, those that lie further off the plane of the circular source trajectory. Performing a reconstruction also for those slices where all voxels are seen at least by 180 degrees will extend the z range and therefore increase the dose usage. In this work a new method is presented that reconstructs also those slices where some or all pixels receive less than 360 degrees but at least 180 degrees of the data. The procedure significantly increases the longitudinal range of the reconstructed volume. As opposed to the existing techniques, the proposed method does not necessitate any multiple convolutions or multiple backprojections, lending itself therefore for a very efficient implementation. To validate the abilities of the extended reconstruction, the authors performed an evaluation of the image quality by using simulated and measured CT data. The method shows good image quality on simulated phantom data as well as on clinical patient scans. Image noise and spatial resolution behave as expected. This means that the noise equals FDK values in the normal region and increases in the extended region due to reduced data redundancies. The extended Feldkamp demonstrates its ability to extend the reconstructable z range and appears to be useful in clinical practice.

A local shift‐variant Fourier model and experimental validation of circular cone‐beam computed tomography artifacts

Large field of view cone-beam computed tomography (CBCT) is being achieved using circular source and detector trajectories. These circular trajectories are known to collect insufficient data for accurate image reconstruction. Although various descriptions of the missing information exist, the manifestation of this lack of data in reconstructed images is generally nonintuitive. One model predicts that the missing information corresponds to a shift-variant cone of missing frequency components. This description implies that artifacts depend on the imaging geometry, as well as the frequency content of the imaged object. In particular, objects with a large proportion of energy distributed over frequency bands that coincide with the missing cone will be most compromised. These predictions were experimentally verified by imaging small, localized objects (acrylic spheres, stacked disks) at varying positions in the object space and observing the frequency spectrums of the reconstructions. Measurements of the internal angle of the missing cone agreed well with theory, indicating a right circular cone for points on the rotation axis, and an oblique, circular cone elsewhere. In the former case, the largest internal angle with respect to the vertical axis corresponds to the (half) cone angle of the CBCT system (typically approximately 5 degrees - 7.5 degrees in IGRT). Object recovery was also found to be strongly dependent on the distribution of the object's frequency spectrum relative to the missing cone, as expected. The observed artifacts were also reproducible via removal of local frequency components, further supporting the theoretical model. Larger objects with differing internal structures (cellular polyurethane, solid acrylic) were also imaged and interpreted with respect to the previous results. Finally, small animal data obtained using a clinical CBCT scanner were observed for evidence of the missing cone. This study provides insight into the influence of incomplete data collection on the appearance of objects imaged in large field of view CBCT.

3D Analytic Cone-Beam Reconstruction for Multiaxial CT Acquisitions

A conventional 3rd generation Computed Tomography (CT) system with a single circular source trajectory is limited in terms of longitudinal scan coverage since extending the scan coverage beyond 40 mm results in significant cone-beam artifacts. A multiaxial CT acquisition is achieved by combining multiple sequential 3rd generation axial scans or by performing a single axial multisource CT scan with multiple longitudinally offset sources. Data from multiple axial scans or multiple sources provide complementary information. For full-scan acquisitions, we present a window-based 3D analytic cone-beam reconstruction algorithm by tessellating data from neighboring axial datasets. We also show that multi-axial CT acquisition can extend the axial scan coverage while minimizing cone-beam artifacts. For half-scan acquisitions, one cannot take advantage of conjugate rays. We propose a cone-angle dependent weighting approach to combine multi-axial half-scan data. We compute the relative contribution from each axial dataset to each voxel based on the X-ray beam collimation, the respective cone-angles, and the spacing between the axial scans. We present numerical experiments to demonstrate that the proposed techniques successfully reduce cone-beam artifacts at very large volumetric coverage.

Development of a cone angle weighted three-dimensional image reconstruction algorithm to reduce cone-beam artefacts

Image reconstruction from cone-beam projections collected along a single circular source trajectory is commonly done using the Feldkamp algorithm, which performs well only with a small cone angle. In this report, we propose an algorithm to reduce cone-beam artefacts by increasing the cone angle by several fold to achieve satisfactory image quality at the same radiation dose. To examine the factors involved in the occurrence of cone-beam artefacts, a microspheres-phantom was arranged longitudinally at different positions and a computer simulation was performed. Due to differences in projection angle, data projected onto the detector surface were projected along trajectories shown as different periodic functions depending on the distance and position from the mid-plane position. Therefore, projection along several detector channels based on different projection data resulting from different periodic functions is considered responsible for the increase in cone-beam artefacts associated with an increase in the distance of reconstruction planes from the mid-plane position. Our recommended algorithm to reduce such artefacts features a change in weighting with respect to projection data obtained at different projection angles, three-dimensional back-projection of corrected projection data. Numerical phantom simulation and real human head origin study (a prototype cone-beam CT) showed that the effect of the reduction in cone-beam artefacts of an object located at the edges was markedly enhanced at reconstruction planes at positions further from the mid-plane position. We propose a projection angle weight-based algorithm to increase the cone angle by several fold to achieve satisfactory image quality at the same radiation dose. These findings confirmed that this algorithm reduces cone-beam artefacts and generates high-quality reconstruction images.

A three-dimensional weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT under a circular source trajectory

The original FDK algorithm proposed for cone beam (CB) image reconstruction under a circular source trajectory has been extensively employed in medical and industrial imaging applications. With increasing cone angle, CB artefacts in images reconstructed by the original FDK algorithm deteriorate, since the circular trajectory does not satisfy the so-called data sufficiency condition (DSC). A few ‘circular plus’ trajectories have been proposed in the past to help the original FDK algorithm to reduce CB artefacts by meeting the DSC. However, the circular trajectory has distinct advantages over other scanning trajectories in practical CT imaging, such as head imaging, breast imaging, cardiac, vascular and perfusion applications. In addition to looking into the DSC, another insight into the CB artefacts existing in the original FDK algorithm is the inconsistency between conjugate rays that are 180° apart in view angle (namely conjugate ray inconsistency). The conjugate ray inconsistency is pixel dependent, varying dramatically over pixels within the image plane to be reconstructed. However, the original FDK algorithm treats all conjugate rays equally, resulting in CB artefacts that can be avoided if appropriate weighting strategies are exercised. Along with an experimental evaluation and verification, a three-dimensional (3D) weighted axial cone beam filtered backprojection (CB-FBP) algorithm is proposed in this paper for image reconstruction in volumetric CT under a circular source trajectory. Without extra trajectories supplemental to the circular trajectory, the proposed algorithm applies 3D weighting on projection data before 3D backprojection to reduce conjugate ray inconsistency by suppressing the contribution from one of the conjugate rays with a larger cone angle. Furthermore, the 3D weighting is dependent on the distance between the reconstruction plane and the central plane determined by the circular trajectory. The proposed 3D weighted axial CB-FBP algorithm can be implemented in either the native CB geometry or the so-called cone-parallel geometry. By taking the cone-parallel geometry as an example, the experimental evaluation shows that, up to a moderate cone angle corresponding to a detector dimension of 64 × 0.625 mm, the CB artefacts can be substantially suppressed by the proposed algorithm, while advantages of the original FDK algorithm, such as the filtered backprojection algorithm structure, 1D ramp filtering and data manipulation efficiency, are maintained.

An error‐reduction‐based algorithm for cone‐beam computed tomography

Image reconstruction from cone-beam projections collected along a single circular source trajectory is commonly done using the Feldkamp algorithm, which performs well only with a small cone angle. In this report, we propose an error-reduction-based algorithm to increase the cone angle by several folds to achieve satisfactory image quality at the same radiation dose. In our scheme, we first reconstruct the object using the Feldkamp algorithm. Then, we synthesize cone-beam projection data from the reconstructed volume in the same geometry, and reconstruct the volume again from the synthesized projections. Finally, these two reconstruction results are combined to reduce the reconstruction error and produce a superior image volume. The merit of this algorithm is demonstrated in numerical simulation.

A filtered backprojection algorithm for cone beam reconstructionusing rotational filtering under helical source trajectory

With the evolution from multi-detector-row CT to cone beam (CB) volumetric CT, maintaining reconstruction accuracy becomes more challenging. To combat the severe artifacts caused by a large cone angle in CB volumetric CT, three-dimensional reconstruction algorithms have to be utilized. In practice, filtered backprojection (FBP) reconstruction algorithms are more desirable due to their computational structure and image generation efficiency. One of the CB-FBP reconstruction algorithms is the well-known FDK algorithm that was originally derived for a circular x-ray source trajectory by heuristically extending its two-dimensional (2-D) counterpart. Later on, a general CB-FBP reconstruction algorithm was derived for noncircular, such as helical, source trajectories. It has been recognized that a filtering operation in the projection data along the tangential direction of a helical x-ray source trajectory can significantly improve the reconstruction accuracy of helical CB volumetric CT. However, the tangential filtering encounters latitudinal data truncation, resulting in degraded noise characteristics or data manipulation inefficiency. A CB-FBP reconstruction algorithm using one-dimensional rotational filtering across detector rows (namely CB-RFBP) is proposed in this paper. Although the proposed CB-RFBP reconstruction algorithm is approximate, it approaches the reconstruction accuracy that can be achieved by exact helical CB-FBP reconstruction algorithms for moderate cone angles. Unlike most exact CB-FBP reconstruction algorithms in which the redundant data are usually discarded, the proposed CB-RFBP reconstruction algorithm make use of all available projection data, resulting in significantly improved noise characteristics and dose efficiency. Moreover, the rotational filtering across detector rows not only survives the so-called long object problem, but also avoids latitudinal data truncation existing in other helical CB-FBP reconstruction algorithm in which a tangential filtering is carried out, providing better noise characteristics, dose efficiency and data manipulation efficiency.

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 Feldkamp's 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.

Comparison of two three-dimensional x-ray cone-beam-reconstruction algorithms with circular source trajectories

We compare two algorithms of three-dimensional (3D) cone-beam tomography: a 3D backprojection algorithm and a Radon algorithm, with a circular source trajectory. We recall the principle of these algorithms and show that when the source trajectory is circular, an exact reconstruction cannot be performed. We evaluate structures that cannot be detected and show that, for each algorithm, assumptions must be made about the object to estimate the missing information. Using simulated data, we measured the modulation transfer function of the two algorithms, evaluated the density resolution, and measured the artifacts due to missing information. We show that the 3D backprojection algorithm has good geometrical resolution along the axis of rotation and that, from the standpoint of density resolution, its useful limit is ±3°. We also show that it is sensitive to the lack of information in the horizontal planes. The useful aperture of the Radon algorithm is ±12°; for apertures lower than this limit, the algorithm is much less sensitive to the lack of information in the horizontal planes than the 3D backprojection algorithm. We present two examples of reconstructions that illustrate the limitations of these algorithms when applied to realistic samples and discuss the limits of using each algorithm when the source trajectory is circular.