Inverse-geometry volumetric CT system with multiple detector arrays for wide field-of-view imaging

Current volumetric computed tomography (CT) methods require seconds to acquire a thick volume (>8 cm) with high resolution. Inverse-geometry CT (IGCT) is a new system geometry under investigation that is anticipated to be able to image a thick volume in a single gantry rotation with isotropic resolution and no cone-beam artifacts. IGCT employs a large array of source spots opposite a smaller detector array. The in-plane field of view (FOV) is primarily determined by the size of the source array, in much the same way that the FOV is determined by the size of the detector array in a conventional CT system. Thus, the size of the source array can be a limitation on the achievable FOV. We propose adding additional detector arrays, spaced apart laterally, to increase the in-plane FOV while still using a modestly sized source array. We determine optimal detector placement to maximize the FOV while obtaining relatively uniform sampling. We also demonstrate low wasted radiation of the proposed system through design and simulation of a pre-patient collimator. Reconstructions from simulated projection data show no artifacts when combining the data from the detector arrays. Finally, to demonstrate feasibility of the concept, an anthropomorphic thorax phantom containing a porcine heart was scanned on a prototype table-top system. The reconstructed axial images demonstrate a 45 cm in-plane FOV using a 23 cm source array.     

A prototype table-top inverse-geometry volumetric CT system

A table-top volumetric CT system has been implemented that is able to image a 5-cm-thick volume in one circular scan with no cone-beam artifacts. The prototype inverse-geometry CT (IGCT) scanner consists of a large-area, scanned x-ray source and a detector array that is smaller in the transverse direction. The IGCT geometry provides sufficient volumetric sampling because the source and detector have the same axial, or slice direction, extent. This paper describes the implementation of the table-top IGCT scanner, which is based on the NexRay Scanning-Beam Digital X-ray system (NexRay, Inc., Los Gatos, CA) and an investigation of the system performance. The alignment and flat-field calibration procedures are described, along with a summary of the reconstruction algorithm. The resolution and noise performance of the prototype IGCT system are studied through experiments and further supported by analytical predictions and simulations. To study the presence of cone-beam artifacts, a "Defrise" phantom was scanned on both the prototype IGCT scanner and a micro CT system with a +/-5 cone angle for a 4.5-cm volume thickness. Images of inner ear specimens are presented and compared to those from clinical CT systems. Results showed that the prototype IGCT system has a 0.25-mm isotropic resolution and that noise comparable to that from a clinical scanner with equivalent spatial resolution is achievable. The measured MTF and noise values agreed reasonably well with theoretical predictions and computer simulations. The IGCT system was able to faithfully reconstruct the laminated pattern of the Defrise phantom while the micro CT system suffered severe cone-beam artifacts for the same object. The inner ear acquisition verified that the IGCT system can image a complex anatomical object, and the resulting images exhibited more high-resolution details than the clinical CT acquisition. Overall, the successful implementation of the prototype system supports the IGCT concept for single-rotation volumetric scanning free from cone-beam artifacts.     

High-quality 3D correction of ring and radiant artifacts in flat panel detector-based cone beam volume CT imaging

The use of an x-ray flat panel detector is increasingly becoming popular in 3D cone beam volume CT machines. Due to the deficient semiconductor array manufacturing process, the cone beam projection data are often corrupted by different types of abnormalities, which cause severe ring and radiant artifacts in a cone beam reconstruction image, and as a result, the diagnostic image quality is degraded. In this paper, a novel technique is presented for the correction of error in the 2D cone beam projections due to abnormalities often observed in 2D x-ray flat panel detectors. Template images are derived from the responses of the detector pixels using their statistical properties and then an effective non-causal derivative-based detection algorithm in 2D space is presented for the detection of defective and mis-calibrated detector elements separately. An image inpainting-based 3D correction scheme is proposed for the estimation of responses of defective detector elements, and the responses of the mis-calibrated detector elements are corrected using the normalization technique. For real-time implementation, a simplification of the proposed off-line method is also suggested. Finally, the proposed algorithms are tested using different real cone beam volume CT images and the experimental results demonstrate that the proposed methods can effectively remove ring and radiant artifacts from cone beam volume CT images compared to other reported techniques in the literature.     

A filtered backprojection algorithm for cone beam reconstruction using 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.     

A new data consistency condition for fan-beam projection data

The sum of all attenuation data acquired in one view of parallel-beam projections is a view angle independent constant. This fact is known as a data consistency condition on the two-dimensional Radon transforms. It plays an important role in tomographic image reconstruction and artifact correction. In this paper, a novel fan-beam data consistency condition (FDCC) is derived and presented. Using the FDCC, individual projection data in one view of fan-beam projections can be estimated from filtering all other projection data measured from different view angles. Numerical simulations are performed to validate the new FDCC in correcting ring artifacts caused by malfunctioning detector cells.     

A three-dimensional-weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT-helical scanning

Based on the structure of the original helical FDK algorithm, a three-dimensional (3D)-weighted cone beam filtered backprojection (CB-FBP) algorithm is proposed for image reconstruction in volumetric CT under helical source trajectory. In addition to its dependence on view and fan angles, the 3D weighting utilizes the cone angle dependency of a ray to improve reconstruction accuracy. The 3D weighting is ray-dependent and the underlying mechanism is to give a favourable weight to the ray with the smaller cone angle out of a pair of conjugate rays but an unfavourable weight to the ray with the larger cone angle out of the conjugate ray pair. The proposed 3D-weighted helical CB-FBP reconstruction algorithm is implemented in the cone-parallel geometry that can improve noise uniformity and image generation speed significantly. Under the cone-parallel geometry, the filtering is naturally carried out along the tangential direction of the helical source trajectory. By exploring the 3D weighting's dependence on cone angle, the proposed helical 3D-weighted CB-FBP reconstruction algorithm can provide significantly improved reconstruction accuracy at moderate cone angle and high helical pitches. The 3D-weighted CB-FBP algorithm is experimentally evaluated by computer-simulated phantoms and phantoms scanned by a diagnostic volumetric CT system with a detector dimension of 64 x 0.625 mm over various helical pitches. The computer simulation study shows that the 3D weighting enables the proposed algorithm to reach reconstruction accuracy comparable to that of exact CB reconstruction algorithms, such as the Katsevich algorithm, under a moderate cone angle (4 degrees) and various helical pitches. Meanwhile, the experimental evaluation using the phantoms scanned by a volumetric CT system shows that the spatial resolution along the z-direction and noise characteristics of the proposed 3D-weighted helical CB-FBP reconstruction algorithm are maintained very well in comparison to the FDK-type algorithms. Moreover, the experimental evaluation by clinical data verifies that the proposed 3D-weighted CB-FBP algorithm for image reconstruction in volumetric CT under helical source trajectory meets the challenges posed by diagnostic applications of volumetric CT imaging.     

基于圆形网格化的磁共振PROPELLER旋转校正算法

PROPELLER数据采集成像技术利用K空间中心重叠采样区域的数据来估计受检查者的运动并加以校正,能较好地消除运动伪影。本文提出了一种基于圆形网格化的PROPELLER旋转校正算法,将中心重叠区域数据网格化到圆形的网格点上,避免了旋转估计时需多次网格化的缺点;并提出有效的相似性测度公式,通过计算测度值估计相应的旋转运动参数,据此对各数据带进行旋转校正。实验表明,与传统旋转校正算法相比,该算法运行速度快,成像质量好。     

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 degrees 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 x 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.     

A short-scan reconstruction for cone-beam CT using shift-invariant FBP and equal weighting

A 3D reconstruction formula has been derived for a circular cone-beam (CB) short scan using ID shift-invariant filtering, CB backprojection, and equal weighting. By first converting the divergent projections to parallel projections, we analyze the circular CB data using the classic central slice theorem. The sampling density in Fourier space is investigated and 1D shift-invariant filtering before backprojection can be used to compensate for the nonuniformity. The final formula consists of a conventional FDK reconstruction and a correction term using differential backprojection and the 1D Hilbert transform in the image domain. On a full scan, the approach reduces to the FDK algorithm, while for a short scan, the CB artifacts are suppressed by the second term. This algorithm outperforms the modified FDK algorithm with Parker's weighting, as illustrated by computer simulations and experimental results. Due to its shift-invariant filtered-backprojection structure, the proposed algorithm is implemented efficiently, and requires a simple adaptation of the FDK algorithm.     

Extension of the reconstruction field of view and truncation correction using sinogram decomposition

We propose a novel truncation correction algorithm that completes unmeasured data outside of the scan field of view, which allows extending the reconstruction field of view. When a patient extends outside the detector coverage the projection data are transversely truncated, which causes severe artifacts. The proposed method utilizes the idea of sinogram decomposition, where we consider sinogram curves corresponding to image points outside the field of view. We propose two ways to estimate the truncated data, one based on the minimum value along the sinogram curve, and the other based on the data values near the edge of truncation. Both estimation methods are combined to achieve uniform image quality improvement from the edge of truncation to the outer side of the extended region. In our evaluation with simulated and real projection data we compare the proposed method with existing methods and investigate the dependence on the amount of truncation. The evaluation shows that the proposed method handles cases when truncation is present on both sides of the detector, or when a high-contrast object is located outside the field of view.     

Evaluation of robustness of maximum likelihood cone-beam CT reconstruction with total variation regularization

The objective of this paper is to evaluate an iterative maximum likelihood (ML) cone-beam computed tomography (CBCT) reconstruction with total variation (TV) regularization with respect to the robustness of the algorithm due to data inconsistencies. Three different and (for clinical application) typical classes of errors are considered for simulated phantom and measured projection data: quantum noise, defect detector pixels and projection matrix errors. To quantify those errors we apply error measures like mean square error, signal-to-noise ratio, contrast-to-noise ratio and streak indicator. These measures are derived from linear signal theory and generalized and applied for nonlinear signal reconstruction. For quality check, we focus on resolution and CT-number linearity based on a Catphan phantom. All comparisons are made versus the clinical standard, the filtered backprojection algorithm (FBP). In our results, we confirm and substantially extend previous results on iterative reconstruction such as massive undersampling of the number of projections. Errors of projection matrix parameters of up to 1° projection angle deviations are still in the tolerance level. Single defect pixels exhibit ring artifacts for each method. However using defect pixel compensation, allows up to 40% of defect pixels for passing the standard clinical quality check. Further, the iterative algorithm is extraordinarily robust in the low photon regime (down to 0.05 mAs) when compared to FPB, allowing for extremely low-dose image acquisitions, a substantial issue when considering daily CBCT imaging for position correction in radiotherapy. We conclude that the ML method studied herein is robust under clinical quality assurance conditions. Consequently, low-dose regime imaging, especially for daily patient localization in radiation therapy is possible without change of the current hardware of the imaging system.     

Three-dimensional reconstruction from cone-beam data in O(N3 log N) time

We have used direct Fourier techniques to modify and implement the 3D reconstruction method from cone-beam projections proposed by Grangeat. In this way we manage to decrease the computational complexity from O(N4) to O(N3 log N). Just as Grangeat's original method is exact in the mathematical sense, so is our method, provided a complete set of projection data is acquired. Also in accordance with Grangeat, our algorithm consists of two distinct phases: phase 1, from cone-beam data to derivatives of Radon data; phase 2, from derivatives of Radon data to reconstructed 3D object. In phase 1 we use the direct Fourier method in reverse to obtain line integrals in the detector plane. In phase 2 the 2D linogram method is employed for reconstruction of vertical and horizontal planes in the Radon space.     

Exact fan-beam and 4pi-acquisition cone-beam SPECT algorithms with uniform attenuation correction

This paper presents analytical fan-beam and cone-beam reconstruction algorithms that compensate for uniform attenuation in single photon emission computed tomography. First, a fan-beam algorithm is developed by obtaining a relationship between the two-dimensional (2D) Fourier transform of parallel-beam projections and fan-beam projections. Using this relationship, 2D Fourier transforms of equivalent parallel-beam projection data are obtained from the fan-beam projection data. Then a quasioptimal analytical reconstruction algorithm for uniformly attenuated Radon data, developed by Metz and Pan, is used to reconstruct the image. A cone-beam algorithm is developed by extending the fan-beam algorithm to 4pi solid angle geometry. The cone-beam algorithm is also an exact algorithm.     

Prior image constrained scatter correction in cone-beam computed tomography image-guided radiation therapy

X-ray scatter is a significant problem in cone-beam computed tomography when thicker objects and larger cone angles are used, as scattered radiation can lead to reduced contrast and CT number inaccuracy. Advances have been made in x-ray computed tomography (CT) by incorporating a high quality prior image into the image reconstruction process. In this paper, we extend this idea to correct scatter-induced shading artifacts in cone-beam CT image-guided radiation therapy. Specifically, this paper presents a new scatter correction algorithm which uses a prior image with low scatter artifacts to reduce shading artifacts in cone-beam CT images acquired under conditions of high scatter. The proposed correction algorithm begins with an empirical hypothesis that the target image can be written as a weighted summation of a series of basis images that are generated by raising the raw cone-beam projection data to different powers, and then, reconstructing using the standard filtered backprojection algorithm. The weight for each basis image is calculated by minimizing the difference between the target image and the prior image. The performance of the scatter correction algorithm is qualitatively and quantitatively evaluated through phantom studies using a Varian 2100 EX System with an on-board imager. Results show that the proposed scatter correction algorithm using a prior image with low scatter artifacts can substantially mitigate scatter-induced shading artifacts in both full-fan and half-fan modes.     

An analytical approach to quantify uniformity artifacts for circular and noncircular detector motion in single photon emission computed tomography imaging

Uniformity artifacts in rotating gamma camera tomography will result if there are errors in the correction factors which are routinely calculated from a static uniformity flood image. The accuracy of the correction factors is a function of the statistics in the collected flood image. Since the factors are applied to each projection view, an error in a correction factor will propagate as a projection error at the same pixel location for each view. For circular detector motion, the error in each projection is reconstructed as a ring whose maximum amplitude varies approximately inversely proportional to the square root of the distance of the projection error from the center of rotation. For noncircular detector motion the artifacts are not rings but are more complicated geometric curves. Simulations show that statistical fluctuations in the reconstructed image will mask the uniformity artifacts provided the correction flood satisfies minimum count requirements. An analytical expression is derived for the percent root-mean-square (% rms) error in the reconstruction and is compared with the percent relative amplitude error (% RAE) of the reconstructed artifacts in order to obtain expressions for uniformity flood counting statistics. For an elliptical source distribution with total counts equal to CT, the uniformity statistics required to reconstruct elliptical disks is inversely proportional to the square root of the area: U greater than or equal to KCT/area 1/2. The constant K depends on the filter function and type of detector motion.     

CT metal artifact reduction method correcting for beam hardening and missing projections

We present and validate a computed tomography (CT) metal artifact reduction method that is effective for a wide spectrum of clinical implant materials. Projections through low-Z implants such as titanium were corrected using a novel physics correction algorithm that reduces beam hardening errors. In the case of high-Z implants (dental fillings, gold, platinum), projections through the implant were considered missing and regularized iterative reconstruction was performed. Both algorithms were combined if multiple implant materials were present. For comparison, a conventional projection interpolation method was implemented. In a blinded and randomized evaluation, ten radiation oncologists ranked the quality of patient scans on which the different methods were applied. For scans that included low-Z implants, the proposed method was ranked as the best method in 90% of the reviews. It was ranked superior to the original reconstruction (p = 0.0008), conventional projection interpolation (p < 0.0001) and regularized limited data reconstruction (p = 0.0002). All reviewers ranked the method first for scans with high-Z implants, and better as compared to the original reconstruction (p < 0.0001) and projection interpolation (p = 0.004). We conclude that effective reduction of CT metal artifacts can be achieved by combining algorithms tailored to specific types of implant materials.     

Cone-beam image reconstruction using spherical harmonics.

Image reconstruction from cone-beam projections is required for both x-ray computed tomography (CT) and single photon emission computed tomography (SPECT). Grangeat's algorithm accurately performs cone-beam reconstruction provided that Tuy's data sufficiency condition is satisfied and projections are complete. The algorithm consists of three stages: (a) Forming weighted plane integrals by calculating the line integrals on the cone-beam detector, and obtaining the first derivative of the plane integrals (3D Radon transform) by taking the derivative of the weighted plane integrals. (b) Rebinning the data and calculating the second derivative with respect to the normal to the plane. (c) Reconstructing the image using the 3D Radon backprojection. A new method for implementing the first stage of Grangeat's algorithm was developed using spherical harmonics. The method assumes that the detector is large enough to image the whole object without truncation. Computer simulations show that if the trajectory of the cone vertex satisfies Tuy's data sufficiency condition, the proposed algorithm provides an exact reconstruction.     

Flat panel detector-based cone beam computed tomography with a circle-plus-two-arcs data acquisition orbit: preliminary phantom study

Cone beam computed tomography (CBCT) has been investigated in the past two decades due to its potential advantages over a fan beam CT. These advantages include (a) great improvement in data acquisition efficiency, spatial resolution, and spatial resolution uniformity, (b) substantially better utilization of x-ray photons generated by the x-ray tube compared to a fan beam CT, and (c) significant advancement in clinical three-dimensional (3D) CT applications. However, most studies of CBCT in the past are focused on cone beam data acquisition theories and reconstruction algorithms. The recent development of x-ray flat panel detectors (FPD) has made CBCT imaging feasible and practical. This paper reports a newly built flat panel detector-based CBCT prototype scanner and presents the results of the preliminary evaluation of the prototype through a phantom study. The prototype consisted of an x-ray tube, a flat panel detector, a GE 8800 CT gantry, a patient table and a computer system. The prototype was constructed by modifying a GE 8800 CT gantry such that both a single-circle cone beam acquisition orbit and a circle-plus-two-arcs orbit can be achieved. With a circle-plus-two-arcs orbit, a complete set of cone beam projection data can be obtained, consisting of a set of circle projections and a set of arc projections. Using the prototype scanner, the set of circle projections were acquired by rotating the x-ray tube and the FPD together on the gantry, and the set of arc projections were obtained by tilting the gantry while the x-ray tube and detector were at the 12 and 6 o'clock positions, respectively. A filtered backprojection exact cone beam reconstruction algorithm based on a circle-plus-two-arcs orbit was used for cone beam reconstruction from both the circle and arc projections. The system was first characterized in terms of the linearity and dynamic range of the detector. Then the uniformity, spatial resolution and low contrast resolution were assessed using different phantoms mainly in the central plane of the cone beam reconstruction. Finally, the reconstruction accuracy of using the circle-plus-two-arcs orbit and its related filtered backprojection cone beam volume CT reconstruction algorithm was evaluated with a specially designed disk phantom. The results obtained using the new cone beam acquisition orbit and the related reconstruction algorithm were compared to those obtained using a single-circle cone beam geometry and Feldkamp's algorithm in terms of reconstruction accuracy. The results of the study demonstrate that the circle-plus-two-arcs cone beam orbit is achievable in practice. Also, the reconstruction accuracy of cone beam reconstruction is significantly improved with the circle-plus-two-arcs orbit and its related exact CB-FPB algorithm, as compared to using a single circle cone beam orbit and Feldkamp's algorithm.     

A z gain nonuniformity correction for multislice volumetric CT scanners

This paper presents a calibration and correction method for detector cell gain variations. A key functionality of current CT scanners is to offer variable slice thickness to the user. To provide this capability in multislice volumetric scanners, while minimizing costs, it is necessary to combine the signals of several detector cells in z, when the desired slice thickness is larger than the minimum provided by a single cell. These combined signals are then pre-amplified, digitized, and transmitted to the system for further processing. The process of combining the output of several detector cells with nonuniform gains can introduce numerical errors when the impinging x-ray signal presents a variation along z over the range of combined cells. These numerical errors, which by nature are scan dependent, can lead to artifacts in the reconstructed images, particularly when the numerical errors vary from channel-to-channel (as the filtered-backprojection filter includes a high-pass filtering along the channel direction, within a given slice). A projection data correction algorithm has been developed to subtract the associated numerical errors. It relies on the ability of calibrating the individual cell gains. For effectiveness and data flow reasons, the algorithm works on a single slice basis, without slice-to-slice exchange of information. An initial error vector is calculated by applying a high-pass filter to the projection data. The essence of the algorithm is to correlate that initial error vector, with a calibration vector obtained by applying the same high-pass filter to various z combinations of the cell gains (each combination representing a basis function for a z expansion). The solution of the least-square problem, obtained via singular value decomposition, gives the coefficients of a polynomial expansion of the signal z slope and curvature. From this information, and given the cell gains, the final error vector is calculated and subtracted from the projection data.