Fan-beam Geometry Research Articles

Dynamic bowtie for fan-beam CT

A bowtie is a filter used to shape an x-ray beam and equalize its flux reaching different detector channels. For development of spectral CT with energy discriminating photon-counting (EDPC) detectors, here we propose and evaluate a dynamic bowtie for performance optimization based on a patient model or a scout scan. With a mechanical rotation of a dynamic bowtie and an adaptive adjustment of an x-ray source flux, an x-ray beam intensity profile can be modulated. First, a mathematical model for dynamic bowtie filtering is established for an elliptical section in fan-beam geometry, and the contour of the optimal bowtie is derived. Then, numerical simulation is performed to compare the performance of the dynamic bowtie in the cases of an ideal phantom and a realistic cross-section relative to the counterparts without any bowtie and with a fixed bowtie respectively. Our dynamic bowtie can equalize the expected numbers of photons in the case of an ideal phantom. In practical cases, our dynamic bowtie can effectively reduce the dynamic range of detected signals inside the field of view. Although our design is optimized for an elliptical phantom, the resultant dynamic bowtie can be applied to a real fan-beam scan if the underlying cross-section can be approximated as an ellipse. Furthermore, our design methodology can be applied to specify an optimized dynamic bowtie for any cross-section of a patient, preferably using rapid prototyping technology.

Visualization Software for CT: Fan/Cone Beam and Metrology Applications

This paper presents the high-performance capabilities developed in specific software for industrial computed tomography (CT) applications. The Technology Center AIMEN has developed in the last years a computed tomography system, in collaboration with the USC, for non-destructive testing and metrology purposes. A visualization tool was implemented for the CT system including 3D rendering and image reconstruction, following the continuous evolution of the system. Image reconstruction accounted for the system's initial fan beam geometry, based on filtered backprojection algorithm. Further development of the CT system with a flat panel detector needed a reconstruction tool for cone beam geometry.Final version of the visualization software accomplishes specialized visualization and applications: reconstruction for different geometries, higher computer memory requirements and CAD and metrology applications in industrial x-ray imaging. This tool has resulted in flexible software with the highest capabilities and further possibilities, adapted to the emerging needs of industrial CT.

Grating-based phase-contrast computed tomography of thick samples

We analyze how the position dependence of the measured signal in phase-contrast imaging using a grating interferometer influences tomographic imaging of samples that are thick in relation to the setup dimensions. The investigations show that there are fundamental differences in image formation depending on the position of the sample relative to the gratings. We discuss tomographic imaging in parallel and fan-beam geometry, with a highlight on tomographic parallel-beam reconstructions for sample positions upstream and downstream of the central beam-splitter grating. Alterations to the standard reconstruction algorithms that result from the position dependence of the measured signal are analyzed analytically and discussed in exemplary computer simulations. We find that the reconstruction results are determined by the position of the axis of rotation relative to the gratings. We conclude that artifact-free reconstructions are feasible for all sample positions within the interferometer, although with different requirements on the angular range and the reconstruction algorithms, respectively.

An improved method for the removal of ring artifacts in high resolution CT imaging

Abstract In high resolution computed tomography (CT) using flat panel detectors, imperfect or defected detector elements cause stripe artifacts in sinogram which results in concentric ring artifacts in the image. Such ring artifacts obscure image details in the regions of interest of the image. In this article, novel techniques are proposed for the detection, classification, and correction of ring artifacts in the sinogram domain. The proposed method is suitable for multislice CT with parallel or fan beam geometry. It can also be employed for ring artifact removal in 3D cone beam volume CT by adopting a sinogram by sinogram processing technique. The detection algorithm is based on applying data driven thresholds on the mean curve and difference curve of the sinogram. The ring artifacts are classified into three types and a separate correction algorithm is used for each class. The performance of the proposed techniques is evaluated on a number of real micro-CT images. Experimental results corroborate that the proposed algorithm can remove ring artifacts from micro-CT images more effectively as compared to other recently reported techniques in the literature.

FDK-Type Algorithms with No Backprojection Weight for Circular and Helical Scan CT.

We develop two Feldkamp-type reconstruction algorithms with no backprojection weight for circular and helical trajectory with planar detector geometry. Advances in solid-state electronic detector technologies lend importance to CT systems with the equispaced linear array, the planar (flat panel) detectors, and the corresponding algorithms. We derive two exact Hilbert filtered backprojection (FBP) reconstruction algorithms with no backprojection weight for 2D fan-beam equispace linear array detector geometry (complement of the equi-angular curved array detector). Based on these algorithms, the Feldkamp-type algorithms with no backprojection weight for 3D reconstruction are developed using the standard heuristic extension of the divergent beam FBP algorithm. The simulation results show that the axial intensity drop in the reconstructed image using the FDK algorithms with no backprojection weight with circular trajectory is similar to that obtained by using Hu's and T-FDK, algorithms. Further, we present efficient algorithms to reduce the axial intensity drop encountered in the standard FDK reconstructions in circular cone-beam CT. The proposed algorithms consist of mainly two steps: reconstruction of the object using FDK algorithm with no backprojection weight and estimation of the missing term. The efficient algorithms are compared with the FDK algorithm, Hu's algorithm, T-FDK, and Zhu et al.'s algorithm in terms of axial intensity drop and noise. Simulation shows that the efficient algorithms give similar performance in axial intensity drop as that of Zhu et al.'s algorithm while one of the efficient algorithms outperforms Zhu et al.'s algorithm in terms of computational complexity.

TH-E-110-04: Relationship Between X-Ray Illumination Volume Size and Flat Field Intensity and Its Impacts on X-Ray Imaging

Purpose: This work investigates the variation of x-ray flat field intensity (I_0) as the illumination volume size changes with different collimator settings, an important phenomenon that is commonly ignored in the current implementations of x-ray volumetric imaging and results in significant reconstruction errors. Methods: A relationship between I_0 and the collimator width is first derived. We propose to calculate the focal spot distribution from flat field projections acquired with different collimator widths. I_0 variation effects on reconstruction and scatter measurement accuracy are evaluated using phantom studies. We compare CT images of an evaluation phantom reconstructed from fan-beam projections using I_0 acquired in fan-beam and cone-beam geometries. Conventional methods measure scatter as the difference between cone-beam and fan-beam projections, which results in measurement errors due to the I_0 variation. We improve the scatter measurement method by considering the I_0 difference in the two projections. Results are compared in projection domain and reconstruction domain. Results: The full width of the measured focal spot distribution is 0.68mm at half maximum, and increases to 2.76mm at 5% maximum. This results in an I_0 value difference up to 17% as the geometry varies from cone-beam to fan-beam, and a reconstruction error of ∼ 20 HU if the I_0 is assumed to be unchanged. The improved scatter measurement method achieves more accurate scatter signals and reduces the reconstruction error from ∼20 HU to less than 6 HU. The method also eliminates the skin-line artifacts with a magnitude of ∼50 HU. Conclusions: The I_0 variation due to large focal spot sizes at low intensities causes CT number inaccuracy and image artifacts, which are often misinterpreted in the current research. Our finding of the I_0 effect identifies one potential error source in the reconstruction, and may facilitate scatter correction algorithm designs which require accurate characterization of scatter signals.

TU‐E‐110‐04: Tetrahedron Beam Computed Tomography

Purpose: The image quality of cone beam CT (CBCT) is significantly inferior to that of diagnostic CT systems. The major problems of CBCT systems include excessive scatter, inferior detector performance, data truncation and approximate cone reconstruction. Its inferior image quality hinders the implementation of advanced IGRT treatment techniques, such as online and offline adaptive radiation treatment (ART). We are developing a novel tetrahedron beam computed tomography (TBCT) system which can significantly improve online image quality, thereby increasing the precision of radiation treatments.Method: A multiple pixel x‐ray source may allow novel imaging systems with improved image quality, reduced x‐ray exposure and lower cost. With a single rotation, the volumes enclosed by a cone (pyramid) and tetrahedron are exactly the same. Hence a volumetric CT scan can also be achieved by rotating a tetrahedron, which is formed by a linear x‐ray source array and a linear detector array orthogonal to each other. In TBCT, scatter photons are mostly rejected thanks to the fan beam geometry. Image quality is further improved by the use of a high quality solid‐state CT detector. Approximate FDK cone reconstruction artifacts can be mitigated using iterative image reconstruction algorithms. Results: A TBCT benchtop system has been developed using a 75 pixel x‐ray tube and an in‐house developed CT detector array. An iterative image reconstruction algorithm has been developed. The system produced excellent CT images which are superior to that of commercial CBCT scanners and close to that of diagnostic CT scanners.Conclusion: TBCT is able to produce image quality close to that of diagnostic CT scanners. Clinical implementation of TBCT in IGRT can improve the precision of radiation treatments. Due to its superior image quality and compact geometry, c‐arm TBCT can also possibly be used as low‐cost, mobile diagnostic CT scanners.

Effect of detector lag on CT noise power spectra

The authors examined the effect of detector lag on the noise power spectrum (NPS) of CT images reconstructed with filtered backprojection (FBP). The authors derived an analytical expression of the NPS with detector lag, and then verified it using computer simulations with parallel beam and fan beam geometries. The dependence of the NPS on the amount of lag, location within the scanned field of view (FOV), and the number of views used in the reconstruction (samples per rotation) was investigated using constant and view dependent noise in the raw data. Detector lag introduces noise correlation in the azimuthal direction. The effect on the NPS is a frequency dependent reduction in amplitude. In small regions of the image, the effect is primarily in the frequencies corresponding to the azimuthal direction. The noise blurring and NPS filtering increases with increasing radial distance, and therefore regions at larger radial distances have lower noise power. With the same detector lag response function, the amount of noise correlation and NPS filtering decreases with increasing number of views. The shape of the NPS depends on the detector lag coefficients, location of the region, and the number of views used in the reconstruction. In general, the noise correlation caused by detector lag decreased the amplitude of the NPS.

Optimized low-kV spectrum of dual-energy CT equipped with high-kV tin filtration for electron density measurements

This paper describes the low-kV spectral optimization of dual-energy CT (DECT) equipped with high-kV tin filtration for the quantitative acquisition of electron density information, which is essential for treatment planning in radiotherapy. In addition, an analytical DECT image simulation was preliminarily performed to demonstrate the effectiveness of the optimized DECT with respect to the beam-hardening reduction. To optimize the low-kV spectrum of DECT, the author calculated the beam-hardening error, CT dose index, and tube loadings for a 50-cm diameter cylindrical water phantom with various combinations of filter materials, a range of thicknesses, and low-kV tube potentials. In addition, a single tube potential of 140 kV filtered by 0.4 mm tin (Sn) was employed for high-kV scanning, as is similar to the commercial implementation of the second-generation dual-source CT scanner. The optimized spectral parameters were then applied to the analytical DECT image simulation using two-dimensional fan-beam geometry for a virtual solid water phantom with 16 bodylike tissue inserts. The author predicts that an optimal low-kV filtration would be 0.144-mm tungsten (W) at 90 kV, as it yields a minimal beam-hardening error with lower tube loadings and dose. The high-kV tube loading and dose obtained using the W filtration were 99 mAs and 2.2 mGy, respectively. These values are nearly equal to those obtained in the case of 2.5 mm Al at 100 kV (100 mAs and 2.3 mGy), which was regarded in this study as a reference filtration; however, the W filtration significantly reduced the beam-hardening error, from 9.5 to 1.4%. The corresponding low-kV tube loading (112 mAs) was five times greater than that of the reference case (21 mAs), but it was maintained at a certain practical level since the low-kV tube loading was comparable to the high-kV tube loading of the reference (100 mAs). The superiority of the beam-hardening reduction is reflected in the simulated images; for example, by the use of the W filter, the beam-hardening-induced deviation between the simulated and theoretical electron density values of cortical bone was reduced from 7.4 to 1.2% as compared with the reference filtration, even though no correction for beam hardening was performed. In terms of beam hardening reduction, the DECT with the low-kV W filtration is more effective for the quantitative measurement of electron density within a practical limit of tube loadings and without additional dose.

Advances in Treatment Techniques

Treatment planning and radiation delivery techniques have advanced significantly during the past 2 decades. The development of the multileaf collimator has changed the scope of radiotherapy. The dynamic conformal arc technique emerged from traditional cone-based conformal arc therapies, which aim to improve target dose uniformity and reduce normal tissue doses. With dynamic conformal arc, the multileaf collimator aperture is shaped dynamically to conform to the target. With the advent of intensity-modulated radiotherapy (IMRT), the concept of arc therapy in combination with IMRT has enabled better-quality dose distributions and more efficient delivery. Helical tomotherapy has been developed to treat targets sequentially by modulating the beam intensity in each "slice" of the patient. Helical tomotherapy offers improved dose distributions for complicated treatments, such as whole-body radiation. Intensity-modulated arc therapy has been studied to modulate fluences in a cone beam rather than fan beam geometry to improve delivery efficiency. This article reviews arc-based IMRT, intensity-modulated arc therapy, and helical tomotherapy techniques. We compare the dosimetric results reported in the literature for each technique in various treatment sites. We also review the application of these techniques in specialized clinical procedures including total marrow irradiation, simultaneous treatment of multiple brain metastases, dose painting, simultaneous integrated boost, and stereotactic radiosurgery.

CT gradient image reconstruction directly from projections

An algorithm is proposed to directly reconstruct a CT gradient image in a region of interest(ROI). First, the central slice theorem is generalized and a differential constraint condition (DCC) is introduced in parallel-beam geometry. Then, an algorithm is developed to reconstruct the gradient images in both Cartesian and polar coordinate systems based on a two-step Hilbert transform method. Finally, the reconstruction algorithm is extended into the equi-distant fan-beam geometry. Meanwhile, a conditional truncation for projection data acquisition is permitted by using a one-dimensional(1-D) finite Hilbert transform in image domain. Because the reconstructed gradient image is in terms of local operator, it have a better performance in CT image analysis and other CT applications compared to the global Calderon operator in Lambda Tomography.

An accurate approximate algorithm for motion compensation in two-dimensional tomography**This work was supported in part by NSF grant DMS-0806304, Toshiba Medical Research Institute, USA and Hubert Curien Laboratory, Jean Monnet University, Saint-Etienne, France.

In this paper, we propose two approximate inversion formulae for motion compensation in tomography: for parallel beam and fan beam geometries. Let denote the operator, which corresponds to the error term of an inversion formula. It is proven that in both cases is bounded; thus, the error term is one order smoother than the original function f in the scale of Sobolev spaces. It is also proven that in both cases if the motion map approaches the identity map, then the norm of approaches zero. The formulae can be easily implemented numerically. Results of numerical experiments in the fan-beam case (which is more common in applications) demonstrate good image quality even when motion is relatively strong.

Flow regime identification and volume fraction prediction in multiphase flows by means of gamma-ray attenuation and artificial neural networks

Abstract This work presents a new methodology for flow regimes identification and volume fraction predictions in water–gas–oil multiphase systems. The approach is based on gamma-ray pulse height distributions (PHDs) pattern recognition by means the artificial neural networks (ANNs). The detection system uses appropriate fan beam geometry, comprised of a dual-energy gamma-ray source and two NaI(Tl) detectors adequately positioned in order measure transmitted and scattered beams, which makes it less dependent on the regime flow. The PHDs are directly used by the ANNs without any parameterization of the measured signal. The system comprises four ANNs. The first identifies the flow regime and the other three ANNs are specialized in volume fraction predictions for each specific regime. The ideal and static theoretical models for annular, stratified and homogeneous regimes have been developed using MCNP-X mathematical code, which was used to provide training, test and validation data for the ANNs. The energy resolution of NaI(Tl) detectors is also considered on the mathematical model. The proposed ANNs could correctly identify all three different regimes with satisfactory prediction of the volume fraction in water–gas–oil multiphase system, demonstrating to be a promising approach for this purpose.

A SPECT reconstruction method for extending parallel to non-parallel geometries

Due to its simplicity, parallel-beam geometry is usually assumed for the development of image reconstruction algorithms. The established reconstruction methodologies are then extended to fan-beam, cone-beam and other non-parallel geometries for practical application. This situation occurs for quantitative SPECT (single photon emission computed tomography) imaging in inverting the attenuated Radon transform. Novikov reported an explicit parallel-beam formula for the inversion of the attenuated Radon transform in 2000. Thereafter, a formula for fan-beam geometry was reported by Bukhgeim and Kazantsev (2002 Preprint N. 99 Sobolev Institute of Mathematics). At the same time, we presented a formula for varying focal-length fan-beam geometry. Sometimes, the reconstruction formula is so implicit that we cannot obtain the explicit reconstruction formula in the non-parallel geometries. In this work, we propose a unified reconstruction framework for extending parallel-beam geometry to any non-parallel geometry using ray-driven techniques. Studies by computer simulations demonstrated the accuracy of the presented unified reconstruction framework for extending parallel-beam to non-parallel geometries in inverting the attenuated Radon transform.

X-ray chest image reconstruction by Radon transform simulation with fan-beam geometry

A Radon transform algorithm which incorporates the correlated X-ray images (some stock chest radiographs) into the processing of back-projection with the fan-beam geometry reconstruction with the aim of improving image quality was developed and explored. These reconstruction images were evaluated and compared with the original image. Meanwhile, we also made the comparisons with the filtered back-projection method and the Radon transform method without fan-beam geometry; the results also reveal that the proposed method has the best image reconstruction capability than other two methods. The results show that the proposed method produces reconstructed images with quiet high peak-signal-to-noise ratio.

Poster — Wed Eve—13: Evaluation of Spectroscopic Compton Tomography Approach at 55 keV

The feasibility of reconstructing 2D electron density () images has been studied. The spectroscopic measurement of Compton scattered photons in a single projection computed tomography (CT) fan beam geometry at 55 keV was investigated. Images were reconstructed by backprojecting over circular paths. A line of energy sensitive detectors was placed outside of periphery of the primary x‐ray fan beam to record the number of scattered photons. The forward problem was simulated in Matlab using analytical equations containing the Klein‐Nishina scattering cross sections, electron density of the object and the solid angle between the point of scattering and the detector. A narrow energy spectrum was needed to achieve good resolution. As the FWHM of the incident spectrum increases, the location where the scatterer can be detected with high precision, decreases. The spatial resolution varies across the image and areas of higher spatial resolution are those which exhibit small angle scattering to the detectors close to the source. Thus various target/filter combinations were studied. The optimal spectrum can be generated by an x‐ray tube operated at 90 kVp with a tungsten target and filter consisting of 0.5mm tungsten and 1.2mm erbium. A point source and ideal detectors were used and no multiple scatter or attenuation was considered. Electron densities were reconstructed using this approach for two phantoms and good qualitative results were obtained. Our ultimate goal is to produce 3D images from scattered photons in a multi‐projection cone‐beam breast CT geometry.

Enhancement of image quality with a fast iterative scatter and beam hardening correction method for kV CBCT

The problem of the enormous amount of scattered radiation in kV CBCT (kilo voltage cone beam computer tomography) is addressed. Scatter causes undesirable streak- and cup-artifacts and results in a quantitative inaccuracy of reconstructed CT numbers, so that an accurate dose calculation might be impossible. Image contrast is also significantly reduced. Therefore we checked whether an appropriate implementation of the fast iterative scatter correction algorithm we have developed for MV (mega voltage) CBCT reduces the scatter contribution in a kV CBCT as well. This scatter correction method is based on a superposition of pre-calculated Monte Carlo generated pencil beam scatter kernels. The algorithm requires only a system calibration by measuring homogeneous slab phantoms with known water-equivalent thicknesses. In this study we compare scatter corrected CBCT images of several phantoms to the fan beam CT images acquired with a reduced cone angle (a slice-thickness of 14 mm in the isocenter) at the same system. Additional measurements at a different CBCT system were made (different energy spectrum and phantom-to-detector distance) and a first order approach of a fast beam hardening correction will be introduced. The observed image quality of the scatter corrected CBCT images is comparable concerning resolution, noise and contrast-to-noise ratio to the images acquired in fan beam geometry. Compared to the CBCT without any corrections the contrast of the contrast-and-resolution phantom with scatter correction and additional beam hardening correction is improved by a factor of about 1.5. The reconstructed attenuation coefficients and the CT numbers of the scatter corrected CBCT images are close to the values of the images acquired in fan beam geometry for the most pronounced tissue types. Only for extreme dense tissue types like cortical bone we see a difference in CT numbers of 5.2%, which can be improved to 4.4% with the additional beam hardening correction. Cupping is reduced from 20% to 4% with scatter correction and 3% with an additional beam hardening correction. After 3 iterations (small phantoms) and 6 to 7 iterations (large phantoms) the algorithm converges. Therefore the algorithm is very fast, that means 1.3 seconds per projection for 3 iterations on a standard PC.

Giant outburst of EXO 2030+375: pulse-phase resolved analysis of INTEGRAL data

In June-September 2006 the Be/X-ray binary EXO 2030+375 experienced the second giant outburst since its discovery. The source was shown to have a complicated pulse-averaged X-ray spectral continuum with possible evidence of cyclotron absorption features. In this paper we present the first pulse-phase resolved analysis of the broad band X-ray spectra of EXO 2030+375 obtained with the INTEGRAL observatory close to the maximum and during the decay phase of the giant outburst. We report a strong variability of the spectrum with pulse phase. Alternative spectral continuum models are discussed. The dependence of the spectral parameters on pulse phase during the maximum of the outburst and the evolution of the pulse profiles with time are qualitatively consistent with the pulsar's emission diagram changing from the fan-beam geometry close to the maximum of the outburst to a combination of pencil and fan beams (of comparable intesities) at the end of the decay phase. Evidence of a cyclotron absorption line around 63 keV at the pulse phase interval preceeding the main peak of the pulse profile is present in the spectrum obtained close to the maximum of the outburst.

Reconstruction From Uniformly Attenuated SPECT Projection Data Using the DBH Method

An algorithm was developed for the 2-D reconstruction of truncated and nontruncated uniformly attenuated data acquired from single photon emission computed tomography (SPECT). The algorithm is able to reconstruct data from half-scan (180 ( degrees ) ) and short-scan (180 ( degrees ) +fan angle) acquisitions for parallel- and fan-beam geometries, respectively, as well as data from full-scan (360 ( degrees )) acquisitions. The algorithm is a derivative, backprojection, and Hilbert transform (DBH) method, which involves the backprojection of differentiated projection data followed by an inversion of the finite weighted Hilbert transform. The kernel of the inverse weighted Hilbert transform is solved numerically using matrix inversion. Numerical simulations confirm that the DBH method provides accurate reconstructions from half-scan and short-scan data, even when there is truncation. However, as the attenuation increases, finer data sampling is required.

Experimental analysis of high-speed gamma-ray tomography performance

High-speed gamma-ray tomography (HSGT) based on multiple fan-beam collimated radioisotope sources has proved to be an efficient and fast method for cross sectional imaging of the dynamics in different industrial processes. The objective of the tomography system described here is to identify the flow regime of gas/liquid pipe flows. The performance of such systems is characterized by the spatial resolution, the speed of response and the measurement resolution of the attenuation coefficient. The work presented here is an experimental analysis of how the measurement geometry and the reconstruction method affect the error of the reconstructed pixel values. These relationships are well established for medical x-ray tomography where high intensity x-ray tubes are used as sources. For radioisotope sources, however, the radiation intensity is limited, which causes the measurement uncertainty, i.e. the Poisson noise, to be considerably higher. In addition, the influence of scattered radiation is more severe in a multiple source radioisotope system compared to that of x-ray systems. A computer-controlled flexible geometry gamma-ray tomograph has been developed to acquire experimental data for different fan-beam measurement geometries, and these data have subsequently been used for image reconstruction using seven different iterative image reconstruction algorithms. The results show that the reconstruction algorithms perform cross sectional images with different quality and that there is virtually nothing to be gained by using more than seven sources for flow regime classification of multiphase pipe flow consisting of gas, oil and water.