Hybrid reconstruction algorithm for x-ray computed tomography

A hybrid reconstruction algorithm (HRA) is derived for fan beam geometry for use with systems utilizing a linear array of detectors. The algorithm uses fan beam geometry with a modified parallel beam reconstruction formula. The parallel beam algorithm is used with fan beam geometry by a simple geometric conversion and a different back projection formula. Correction for center of rotation shift is done during the back projection. Computer simulations are shown, both with the center of rotation shift uncorrected and corrected.     

K-edge imaging in x-ray computed tomography using multi-bin photon counting detectors

After passage through matter, the energy spectrum of a polychromatic beam of x-rays contains valuable information about the elemental composition of the absorber. Conventional x-ray systems or x-ray computed tomography (CT) systems, equipped with scintillator detectors operated in the integrating mode, are largely insensitive to this type of spectral information, since the detector output is proportional to the energy fluence integrated over the whole spectrum. The main purpose of this paper is to investigate to which extent energy-sensitive photon counting devices, operated in the pulse-mode, are capable of revealing quantitative information about the elemental composition of the absorber. We focus on the detection of element-specific, K-edge discontinuities of the photo-electric cross-section. To be specific, we address the question of measuring and imaging the local density of a gadolinium-based contrast agent, in the framework of a generalized dual-energy pre-processing. Our results are very promising and seem to open up new possibilities for the imaging of the distribution of elements with a high atomic number Z in the human body using x-ray attenuation measurements. To demonstrate the usefulness of the detection and the appropriate processing of the spectral information, we present simulated images of an artherosclerotic coronary vessel filled with gadolinium-based contrast agent. While conventional systems, equipped with integrating detectors, often fail to differentiate between contrast filled lumen and artherosclerotic plaque, the use of an energy-selective detection system based on the counting of individual photons reveals a strong contrast between plaque and contrast agent.     

Statistical reconstruction for x-ray CT systems with non-continuous detectors

We analyse the performance of statistical reconstruction (SR) methods when applied to non-continuous x-ray detectors. Robustness to projection gaps is required in x-ray CT systems with multiple detector modules or with defective detector pixels. In such situations, the advantage of statistical reconstruction is that it is able to ignore missing or faulty pixels and that it makes optimal use of the remaining line integrals. This potentially obviates the need to fill the sinogram discontinuities by interpolation or any other approximative pre-processing techniques. In this paper, we apply SR to cone beam projections of (i) a hypothetical modular detector micro-CT scanner and of (ii) a system with randomly located defective detector elements. For the modular-detector system, SR produces reconstruction volumes free of noticeable gap-induced artefacts as long as the location of detector gaps and selection of the scanning range provide complete object sampling in the central imaging plane. When applied to randomly located faulty detector elements, SR produces images free of substantial ring artefacts even for cases where defective pixels cover as much as 3% of the detector area.     

Approximate analytic reconstruction in x-ray fluorescence computed tomography

X-ray fluorescence computed tomography (XFCT) is an emerging imaging modality that allows for the reconstruction of the distribution of nonradioactive elements within a sample from measurements of fluorescence x-rays produced by irradiation of the sample with monochromatic synchrotron radiation. XFCT is not a transmission tomography modality, but rather a stimulated emission tomography modality and thus correction for attenuation of the incident and fluorescence photons is essential if accurate images are to be obtained. In this work, we develop and characterize an approximate analytic approach to image reconstruction with attenuation correction in XFCT that is applicable when the incident beam attenuation is uniform and when a factor involving fluorescence attenuation and solid angle effects satisfies a certain approximation. When these conditions hold, we demonstrate that the XFCT imaging equation reduces to the exponential Radon transform, which can be readily inverted. The necessary approximation worsens as the total fluorescence attenuation in the sample grows, but the approach is found to be relatively robust as the approximation breaks down. In a long-axis, small solid angle geometry the proposed approach performs comparably to a previously proposed, more computationally expensive approximate method across a range of attenuation levels. In a short-axis, large solid angle geometry, the proposed approach is found to outperform this previous method.     

Step-and-shoot data acquisition and reconstruction for cardiac x-ray computed tomography

Coronary artery imaging with x-ray computed tomography (CT) is one of the most recent advancements in CT clinical applications. Although existing "state-of-the-art" clinical protocols today utilize helical data acquisition, it suffers from the lack of ability to handle irregular heart rate and relatively high x-ray dose to patients. In this paper, we propose a step-and-shoot data acquisition protocol that significantly overcomes these shortcomings. The key to the proposed protocol is the large volume coverage (40 mm) enabled by the cone beam CT scanner, which allows the coverage of the entire heart in 3 to 4 steps. In addition, we propose a gated complementary reconstruction algorithm that overcomes the longitudinal truncation problem resulting from the cone beam geometry. Computer simulations, phantom experiments, and clinical studies were conducted to validate our approach.     

Segmentation-free statistical image reconstruction for polyenergetic x-ray computed tomography with experimental validation

This paper describes a statistical image reconstruction method for x-ray CT that is based on a physical model that accounts for the polyenergetic x-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. Unlike our earlier work, the proposed algorithm does not require pre-segmentation of the object into the various tissue classes (e.g., bone and soft tissue) and allows mixed pixels. The attenuation coefficient of each voxel is modelled as the product of its unknown density and a weighted sum of energy-dependent mass attenuation coefficients. We formulate a penalized-likelihood function for this polyenergetic model and develop an iterative algorithm for estimating the unknown density of each voxel. Applying this method to simulated x-ray CT measurements of objects containing both bone and soft tissue yields images with significantly reduced beam hardening artefacts relative to conventional beam hardening correction methods. We also apply the method to real data acquired from a phantom containing various concentrations of potassium phosphate solution. The algorithm reconstructs an image with accurate density values for the different concentrations, demonstrating its potential for quantitative CT applications.     

Quantitative bone measurements using x-ray computed tomography with second-order correction

Two-component cortical bone and water, and trabecular bone and water models were used to study the beam hardening errors associated with computed tomography (CT) bone densitometry and sizing methods. Specimens used included a femur, humerus, radius, ulna, and vertebral bodies. A second-order correction algorithm was employed to improve the accuracy of these quantitative CT methods. Physical measurements of the bones were obtained to verify the CT results. Large discrepancies were found between the uncorrected and second-order corrected CT assessments of cortical bone density, trabecular bone density, water density within the medullary canal, total bone area, medullary canal area, and cortical area. The interosseous lucent streak was also quantitatively studied. Results showed that second-order correction significantly improved the accuracy of CT bone densitometry and sizing methods.     

Quasimonochromatic x-ray computed tomography by the balanced filter method using a conventional x-ray source

A quasimonochromatic x-ray computed tomography (CT) system utilizing balanced filters has recently been developed for acquiring quantitative CT images. This system consisted of basic components such as a conventional x-ray generator for radiography, a stage for mounting and rotating objects, and an x-ray line sensor camera. Metallic sheets of Er and Yb were used as the balanced filters for obtaining quasimonochromatic incident x rays that include the characteristic lines of the W Kalpha doublet from a tungsten target. The mean energy and energy width of the quasimonochromatic x rays were determined to be 59.0 and 1.9 keV, respectively, from x-ray spectroscopic measurements using a high-purity Ge detector. The usefulness of the present x-ray CT system was demonstrated by obtaining spatial distributions of the linear attenuation coefficients of three selected samples--a 20 cm diameter cylindrical water phantom, a 3.5 cm diameter aluminum rod, and a human head phantom. The results clearly indicate that this apparatus is surprisingly effective for estimating the distribution of the linear attenuation coefficients without any correction of the beam-hardening effect. Thus, implementing the balanced filter method on an x-ray CT scanner has promise in producing highly quantitative CT images.     

Statistical image reconstruction for transmission tomography using relaxed ordered subset algorithms

Statistical reconstruction methods offer possibilities for improving image quality as compared to analytical methods, but current reconstruction times prohibit routine clinical applications in x-ray computed tomography (CT). To reduce reconstruction times, we have applied (under) relaxation to ordered subset algorithms. This enables us to use subsets consisting of only single projection angle, effectively increasing the number of image updates within an entire iteration. A second advantage of applying relaxation is that it can help improve convergence by removing the limit cycle behaviour of ordered subset algorithms, which normally do not converge to an optimal solution but rather a suboptimal limit cycle consisting of as many points as there are subsets. Relaxation suppresses the limit cycle behaviour by decreasing the stepsize for approaching the solution. A simulation study for a 2D mathematical phantom and three different ordered subset algorithms shows that all three algorithms benefit from relaxation: equal noise-to-resolution trade-off can be achieved using fewer iterations than the conventional algorithms, while a lower minimal normalized mean square error (NMSE) clearly indicates a better convergence. Two different schemes for setting the relaxation parameter are studied, and both schemes yield approximately the same minimal NMSE.     

Polymer gel dosimetry using x-ray computed tomography: a feasibility study

A new three-dimensional dosimetry technique using x-ray computed tomography (CT) to analyse polymer gels is proposed. The CT imaging is sensitive to radiation-induced density changes that occur within irradiated polyacrylamide gel (PAG). In this preliminary study, a CT imaging protocol is developed to optimize CT images of PAG; the response of PAG CT number to dose (N(CT)-dose response) and the reproducibility of the response are investigated, and the use of CT to analyse PAG is compared with MRI. Experiments were conducted using two 1.5 l cylindrical PAG phantoms (3% acrylamide, 3% bis and 5% gelatin by weight), one irradiated with four intersecting 10 MV photon beams and the other with 10 sets of 6 MV parallel opposed circular radiosurgery fields. The final imaging protocol involves using optimum CT parameters (120 kVp and 200 mAs for our GE HiSpeed CT/i scanner), image averaging and background subtraction. The N(CT)-dose response is reproducible, linear up to 800-1000 cGy and is relatively insensitive to the gel temperature during imaging. The dose resolution is approximately 50 cGy for an image thickness of 10 mm. Despite the low dose resolution, preliminary results indicate that this CT technique provides accurate localization of high dose gradients such as those observed in stereotactic radiosurgery. Thus, given the availability and speed of CT scanners, the technique has the potential to be a valuable and practical 3D dose verification tool in radiation therapy.     

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.     

Eigenvector decomposition of full-spectrum x-ray computed tomography

Energy-discriminated x-ray computed tomography (CT) data were projected onto a set of basis functions to suppress the noise in filtered back-projection (FBP) reconstructions. The x-ray CT data were acquired using a novel x-ray system which incorporated a single-pixel photon-counting x-ray detector to measure the x-ray spectrum for each projection ray. A matrix of the spectral response of different materials was decomposed using eigenvalue decomposition to form the basis functions. Projection of FBP onto basis functions created a de facto image segmentation of multiple contrast agents. Final reconstructions showed significant noise suppression while preserving important energy-axis data. The noise suppression was demonstrated by a marked improvement in the signal-to-noise ratio (SNR) along the energy axis for multiple regions of interest in the reconstructed images. Basis functions used on a more coarsely sampled energy axis still showed an improved SNR. We conclude that the noise-resolution trade off along the energy axis was significantly improved using the eigenvalue decomposition basis functions.     

Iterative concurrent reconstruction algorithms for emission computed tomography

Direct reconstruction techniques, such as those based on filtered backprojection, are typically used for emission computed tomography (ECT), even though it has been argued that iterative reconstruction methods may produce better clinical images. The major disadvantage of iterative reconstruction algorithms, and a significant reason for their lack of clinical acceptance, is their computational burden. We outline a new class of 'concurrent' iterative reconstruction techniques for ECT in which the reconstruction process is reorganized such that a significant fraction of the computational processing occurs concurrently with the acquisition of ECT projection data. These new algorithms use the 10-30 min required for acquisition of a typical SPECT scan to iteratively process the available projection data, significantly reducing the requirements for post-acquisition processing. These algorithms are tested on SPECT projection data from a Hoffman brain phantom acquired with a 2 x 10(5) counts in 64 views each having 64 projections. The SPECT images are reconstructed as 64 x 64 tomograms, starting with six angular views. Other angular views are added to the reconstruction process sequentially, in a manner that reflects their availability for a typical acquisition protocol. The results suggest that if T s of concurrent processing are used, the reconstruction processing time required after completion of the data acquisition can be reduced by at least 1/3T s.     

General surface reconstruction for cone-beam multislice spiral computed tomography

A new family of cone-beam reconstruction algorithm, the General Surface Reconstruction (GSR), is proposed and formulated in this paper for multislice spiral computed tomography (CT) reconstructions. It provides a general framework to allow the reconstruction of planar or nonplanar surfaces on a set of rebinned short-scan parallel beam projection data. An iterative surface formation method is proposed as an example to show the possibility to form nonplanar reconstruction surfaces to minimize the adverse effect between the collected cone-beam projection data and the reconstruction surfaces. The improvement in accuracy of the nonplanar surfaces over planar surfaces in the two-dimensional approximate cone-beam reconstructions is mathematically proved and demonstrated using numerical simulations. The proposed GSR algorithm is evaluated by the computer simulation of cone-beam spiral scanning geometry and various mathematical phantoms. The results demonstrate that the GSR algorithm generates much better image quality compared to conventional multislice reconstruction algorithms. For a table speed up to 100 mm per rotation, GSR demonstrates good image quality for both the low-contrast ball phantom and thorax phantom. All other performance parameters are comparable to the single-slice 180 degrees LI (linear interpolation) algorithm, which is considered the "gold standard." GSR also achieves high computing efficiency and good temporal resolution, making it an attractive alternative for the reconstruction of next generation multislice spiral CT data.     

Image reconstruction for fan-beam differential phase contrast computed tomography

Recently, x-ray differential phase contrast computed tomography (DPC-CT) has been experimentally implemented using a conventional tube combined with gratings. Images were reconstructed using a parallel-beam reconstruction formula. However, parallel-beam reconstruction formulae are not applicable when the parallel-beam approximation fails. In this paper, we present a new image reconstruction formula for fan-beam DPC-CT. There are several novel features of the new image reconstruction formula: (i) when the scanning angular range of data acquisition is larger than pi + gamma(m) (gamma(m) is the full fan angle), the entire field of view can be exactly reconstructed; (ii) when the scanning angular range is smaller than pi + gamma(m), a local region of interest (ROI) can be exactly reconstructed; (iii) it enables an exact reconstruction for a local ROI when the projection data are truncated at some view angles; (iv) it enlarges the imaging field of view when the detector is asymmetrically placed. In this last case, the data are truncated from every view angle. Numerical simulations have been conducted to validate the new reconstruction formula.     

Analysis of x-ray computed tomography images using the noise power spectrum and autocorrelation function

A discrete representation of the reconstruction process, consistent with the method of data collection, has been used to derive expressions for the noise power spectrum, autocorrelation function and noise equivalent quanta (NEQ) of a computed tomography (CT) image. These parameters have been expressed in terms of basic scanning factors such as tube current, exposure time, slice width and number of detectors. Each of these factors affects the overall magnitude of the noise power spectrum, but the spatial frequency dependence is also determined by the type of reconstruction filter used in the computer algorithm. The noise power spectrum has been calculated for scanners employing either a ramp or Hanning weighted ramp filter. Predictions made from this theoretical analysis have been compared with experimental measurements made on various CT scanners. Measurements were made of the modulation transfer function (MTF) by techniques which permitted us to deduce the contributions of the algorithmic and non-algorithmic components to the overall MTF. NEQ values have been calculated for a number of CT scanners.