Exact and approximate algorithms for helical cone-beam CT

Deep learning enabled ultra-fast-pitch acquisition in clinical X-ray computed tomography

OBJECTIVE

In X-raycomputed tomography (CT), many important clinical applications may benefit from a fast acquisition speed. The helical scan is the most widely used acquisition mode in clinical CT, where a fast helical pitch can improve the acquisition speed. However, on a typical single-source helical CT (SSCT) system, the helical pitch p typically cannot exceed 1.5; otherwise, reconstruction artifacts will result from data insufficiency. The purpose of this work is to develop a deep convolutional neural network (CNN) to correct for artifacts caused by an ultra-fast pitch, which can enable faster acquisition speed than what is currently achievable.

METHODS

A customized CNN (denoted as ultra-fast-pitch network (UFP-net)) was developed to restore the underlying anatomical structure from the artifact-corrupted post-reconstruction data acquired from SSCT with ultra-fast pitch (i.e., p ≥ 2). UFP-net employed residual learning to capture the features of image artifacts. UFP-net further deployed in-house-customized functional blocks with spatial-domain local operators and frequency-domain non-local operators, to explore multi-scale feature representation. Images of contrast-enhanced patient exams (n = 83) with routine pitch setting (i.e., p < 1) were retrospectively collected, which were used as training and testing datasets. This patient cohort involved CT exams over different scan ranges of anatomy (chest, abdomen, and pelvis) and CT systems (Siemens Definition, Definition Flash, Definition AS+, Siemens Healthcare, Inc.), and the corresponding base CT scanning protocols used consistent settings of major scan parameters (e.g., collimation and pitch). Forward projection of the original images was calculated to synthesize helical CT scans with one regular pitch setting (p = 1) and two ultra-fast-pitch setting (p = 2 and 3). All patient images were reconstructed using the standard filtered-back-projection (FBP) algorithm. A customized multi-stage training scheme was developed to incrementally optimize the parameters of UFP-net, using ultra-fast-pitch images as network inputs and regular pitch images as labels. Visual inspection was conducted to evaluate image quality. Structural similarity index (SSIM) and relative root-mean-square error (rRMSE) were used as quantitative quality metrics.

RESULTS

The UFP-net dramatically improved image quality over standard FBP at both ultra-fast-pitch settings. At p = 2, UFP-net yielded higher mean SSIM (> 0.98) with lower mean rRMSE (< 2.9%), compared to FBP (mean SSIM < 0.93; mean rRMSE > 9.1%). Quantitative metrics at p = 3: UFP-net-mean SSIM [0.86, 0.94] and mean rRMSE [5.0%, 8.2%]; FBP-mean SSIM [0.36, 0.61] and mean rRMSE [36.0%, 58.6%].

CONCLUSION

The proposed UFP-net has the potential to enable ultra-fast data acquisition in clinical CT without sacrificing image quality. This method has demonstrated reasonable generalizability over different body parts when the corresponding CT exams involved consistent base scan parameters.

Head Motion Correction Based on Filtered Backprojection in Helical CT Scanning

Head motion may unexpectedly occur during a CT scan. It thereby results in motion artifacts in a reconstructed image and may lead to a false diagnosis or a failure of diagnosis. To alleviate this motion problem, as a hardware approach, increasing the gantry rotation speed or using an immobilization device is usually considered. These approaches, however, cannot completely resolve the motion problem. Hence, motion estimation (ME) and compensation for it have been explored as a software approach instead. In this paper, adopting the latter approach, we propose a head motion correction algorithm in helical CT scanning, based on filtered backprojection (FBP). For the motion correction, we first introduce a new motion-compensated (MC) reconstruction scheme based on FBP, which is applicable to helical scanning. We then estimate the head motion parameters by using an iterative nonlinear optimization algorithm, or the L-BFGS. Note here that an objective function for the optimization is defined on reconstructed images in each iteration, which are obtained by using the proposed MC reconstruction scheme. Using the estimated motion parameters, we then obtain the final MC reconstructed image. Using numerical and physical phantom datasets along with simulated head motions, we demonstrate that the proposed algorithm can provide significantly improved quality to MC reconstructed images by alleviating motion artifacts.

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

GOALS

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.

METHODS

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.

RESULTS

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.

CONCLUSION

The preliminary data show that the proposed algorithm performs as well as the 3-D weighted CB-FBP algorithm in the cone-parallel geometry.

SIGNIFICANCE

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.

Technical Note: FreeCT_wFBP: A robust, efficient, open-source implementation of weighted filtered backprojection for helical, fan-beam CT

PURPOSE

With growing interest in quantitative imaging, radiomics, and CAD using CT imaging, the need to explore the impacts of acquisition and reconstruction parameters has grown. This usually requires extensive access to the scanner on which the data were acquired and its workflow is not designed for large-scale reconstruction projects. Therefore, the authors have developed a freely available, open-source software package implementing a common reconstruction method, weighted filtered backprojection (wFBP), for helical fan-beam CT applications.

METHODS

FreeCT_wFBP is a low-dependency, GPU-based reconstruction program utilizing c for the host code and Nvidia CUDA C for GPU code. The software is capable of reconstructing helical scans acquired with arbitrary pitch-values, and sampling techniques such as flying focal spots and a quarter-detector offset. In this work, the software has been described and evaluated for reconstruction speed, image quality, and accuracy. Speed was evaluated based on acquisitions of the ACR CT accreditation phantom under four different flying focal spot configurations. Image quality was assessed using the same phantom by evaluating CT number accuracy, uniformity, and contrast to noise ratio (CNR). Finally, reconstructed mass-attenuation coefficient accuracy was evaluated using a simulated scan of a FORBILD thorax phantom and comparing reconstructed values to the known phantom values.

RESULTS

The average reconstruction time evaluated under all flying focal spot configurations was found to be 17.4 ± 1.0 s for a 512 row × 512 column × 32 slice volume. Reconstructions of the ACR phantom were found to meet all CT Accreditation Program criteria including CT number, CNR, and uniformity tests. Finally, reconstructed mass-attenuation coefficient values of water within the FORBILD thorax phantom agreed with original phantom values to within 0.0001 mm(2)/g (0.01%).

CONCLUSIONS

FreeCT_wFBP is a fast, highly configurable reconstruction package for third-generation CT available under the GNU GPL. It shows good performance with both clinical and simulated data.

Optimization of an on-board imaging system for extremely rapid radiation therapy

PURPOSE

Next-generation extremely rapid radiation therapy systems could mitigate the need for motion management, improve patient comfort during the treatment, and increase patient throughput for cost effectiveness. Such systems require an on-board imaging system that is competitively priced, fast, and of sufficiently high quality to allow good registration between the image taken on the day of treatment and the image taken the day of treatment planning. In this study, three different detectors for a custom on-board CT system were investigated to select the best design for integration with an extremely rapid radiation therapy system.

METHODS

Three different CT detectors are proposed: low-resolution (all 4×4 mm pixels), medium-resolution (a combination of 4×4 mm pixels and 2×2 mm pixels), and high-resolution (all 1×1 mm pixels). An in-house program was used to generate projection images of a numerical anthropomorphic phantom and to reconstruct the projections into CT datasets, henceforth called "realistic" images. Scatter was calculated using a separate Monte Carlo simulation, and the model included an antiscatter grid and bowtie filter. Diagnostic-quality images of the phantom were generated to represent the patient scan at the time of treatment planning. Commercial deformable registration software was used to register the diagnostic-quality scan to images produced by the various on-board detector configurations. The deformation fields were compared against a "gold standard" deformation field generated by registering initial and deformed images of the numerical phantoms that were used to make the diagnostic and treatment-day images. Registrations of on-board imaging system data were judged by the amount their deformation fields differed from the corresponding gold standard deformation fields--the smaller the difference, the better the system. To evaluate the registrations, the pointwise distance between gold standard and realistic registration deformation fields was computed.

RESULTS

By most global metrics (e.g., mean, median, and maximum pointwise distance), the high-resolution detector had the best performance but the medium-resolution detector was comparable. For all medium- and high-resolution detector registrations, mean error between the realistic and gold standard deformation fields was less than 4 mm. By pointwise metrics (e.g., tracking a small lesion), the high- and medium-resolution detectors performed similarly. For these detectors, the smallest error between the realistic and gold standard registrations was 0.6 mm and the largest error was 3.6 mm.

CONCLUSIONS

The medium-resolution CT detector was selected as the best for an extremely rapid radiation therapy system. In essentially all test cases, data from this detector produced a significantly better registration than data from the low-resolution detector and a comparable registration to data from the high-resolution detector. The medium-resolution detector provides an appropriate compromise between registration accuracy and system cost.

Frequency split metal artifact reduction (FSMAR) in computed tomography

PURPOSE

The problem of metal artifact reduction (MAR) is almost as old as the clinical use of computed tomography itself. When metal implants are present in the field of measurement, severe artifacts degrade the image quality and the diagnostic value of CT images. Up to now, no generally accepted solution to this issue has been found. In this work, a method based on a new MAR concept is presented: frequency split metal artifact reduction (FSMAR). It ensures efficient reduction of metal artifacts at high image quality with enhanced preservation of details close to metal implants.

METHODS

FSMAR combines a raw data inpainting-based MAR method with an image-based frequency split approach. Many typical methods for metal artifact reduction are inpainting-based MAR methods and simply replace unreliable parts of the projection data, for example, by linear interpolation. Frequency split approaches were used in CT, for example, by combining two reconstruction methods in order to reduce cone-beam artifacts. FSMAR combines the high frequencies of an uncorrected image, where all available data were used for the reconstruction with the more reliable low frequencies of an image which was corrected with an inpainting-based MAR method. The algorithm is tested in combination with normalized metal artifact reduction (NMAR) and with a standard inpainting-based MAR approach. NMAR is a more sophisticated inpainting-based MAR method, which introduces less new artifacts which may result from interpolation errors. A quantitative evaluation was performed using the examples of a simulation of the XCAT phantom and a scan of a spine phantom. Further evaluation includes patients with different types of metal implants: hip prostheses, dental fillings, neurocoil, and spine fixation, which were scanned with a modern clinical dual source CT scanner.

RESULTS

FSMAR ensures sharp edges and a preservation of anatomical details which is in many cases better than after applying an inpainting-based MAR method only. In contrast to other MAR methods, FSMAR yields images without the usual blurring close to implants.

CONCLUSIONS

FSMAR should be used together with NMAR, a combination which ensures an accurate correction of both high and low frequencies. The algorithm is computationally inexpensive compared to iterative methods and methods with complex inpainting schemes. No parameters were chosen manually; it is ready for an application in clinical routine.

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.

Accurate helical cone-beam CT reconstruction with redundant data

We present a new image reconstruction algorithm for helical cone-beam computed tomography (CT). This algorithm is designed for data collected at or near maximum pitch, and provides a theoretically exact and stable reconstruction while beneficially using all measured data. The main operations involved are a differentiated backprojection and a finite-support Hilbert transform inversion. These operations are applied onto M-lines, and the beneficial use of all measured data is gained from averaging three volumes reconstructed each with a different choice of M-lines. The technique is overall similar to that presented by one of the authors in a previous publication, but operates volume-wise, instead of voxel-wise, which yields a significantly more efficient reconstruction procedure. The algorithm is presented in detail. Also, preliminary results from computer-simulated data are provided to demonstrate the numerical stability of the algorithm, the beneficial use of redundant data and the ability to process data collected with an angular flying focal spot.

Optimized reconstruction algorithm for helical CT with fractional pitch between 1PI and 3PI

We propose an approximate approach to use redundant data outside the 1PI window within the exact Katsevich reconstruction framework. The proposed algorithm allows a flexible selection of the helical pitch, which is useful for clinical applications. Our idea is an extension of the one proposed by KOhler, Bontus, and Koken (2006). It is based on optimizing the contribution weights of convolution families used in exact Katsevich 3PI algorithms, so that the total weight of each Radon plane is as close to 1 as possible. Optimization is based on solving a least squares problem subject to linear constrains. Numerical evaluation shows good noise and artifact reduction properties of the proposed algorithm.

Isotropic CT examination of abdomen and pelvis diagnostic quality of reformat

RATIONALE AND OBJECTIVES

To evaluate the image quality of axial and coronal reformats obtained from isotropic resolution abdomino-pelvic computed tomography (CT) examinations.

MATERIALS AND METHODS

Thirty consecutive patients with intravenous contrast-enhanced abdomino-pelvic CT examinations (Brilliance 40, Philips Medical Systems, Cleveland, OH) were enrolled for the study. The raw data were reconstructed into two sets of source axial images: 0.9-mm slice widths with 0.45-mm reconstruction interval (isotropic resolution) and 4-mm slice widths with 3-mm reconstruction interval (anisotropic resolution: group A). Isotropic data set was reformatted into axial and coronal stacks (groups B and C, respectively) with 4-mm slice width and 3-mm interval. Three independent readers evaluated stacks A to C using a 3-point scale for resolution of hepatic vessels, edge sharpness of kidneys, respiratory motion artifact, reconstruction artifact, noise, and overall image quality.

RESULTS

There was no statistical difference among the groups A to C for vessel resolution, motion artifact, noise, and overall quality. The scores given to group C were significantly lower than those to groups A and B for reconstruction artifacts. There was no difference among groups A to C for overall impression of image quality. The interreader agreements were excellent for axial images (groups A and B) and moderate for coronal reformats.

CONCLUSION

Isotropic scanning of the abdomen and pelvis allows creation of reformats with similar image quality as similar thickness axial source images. These reformats are of sufficient quality to form the basis of clinical interpretation.

Analysis of Cone-Beam Artifacts in off-Centered Circular CT for Four Reconstruction Methods

Cone-beam (CB) acquisition is increasingly used for truly three-dimensional X-ray computerized tomography (CT). However, tomographic reconstruction from data collected along a circular trajectory with the popular Feldkamp algorithm is known to produce the so-called CB artifacts. These artifacts result from the incompleteness of the source trajectory and the resulting missing data in the Radon space increasing with the distance to the plane containing the source orbit. In the context of the development of integrated PET/CT microscanners, we introduced a novel off-centered circular CT cone-beam geometry. We proposed a generalized Feldkamp formula (α-FDK) adapted to this geometry, but reconstructions suffer from increased CB artifacts. In this paper, we evaluate and compare four different reconstruction methods for correcting CB artifacts in off-centered geometry. We consider the α-FDK algorithm, the shift-variant FBP method derived from the T-FDK, an FBP method based on the Grangeat formula, and an iterative algebraic method (SART). The results show that the low contrast artifacts can be efficiently corrected by the shift-variant method and the SART method to achieve good quality images at the expense of increased computation time, but the geometrical deformations are still not compensated for by these techniques.

Direct cone-beam cardiac reconstruction algorithm with cardiac banding artifact correction

Multislice helical computed tomography (CT) is a promising noninvasive technique for coronary artery imaging. Various factors can cause inconsistencies in cardiac CT data, which can result in degraded image quality. These inconsistencies may be the result of the patient physiology (e.g., heart rate variations), the nature of the data (e.g., cone-angle), or the reconstruction algorithm itself. An algorithm which provides the best temporal resolution for each slice, for example, often provides suboptimal image quality for the entire volume since the cardiac temporal resolution (TRc) changes from slice to slice. Such variations in TRc can generate strong banding artifacts in multiplanar reconstruction images or three-dimensional images. Discontinuous heart walls and coronary arteries may compromise the accuracy of the diagnosis. A beta-blocker is often used to reduce and stabilize patients' heart rate but cannot eliminate the variation. In order to obtain robust and optimal image quality, a software solution that increases the temporal resolution and decreases the effect of heart rate is highly desirable. This paper proposes an ECG-correlated direct cone-beam reconstruction algorithm (TCOT-EGR) with cardiac banding artifact correction (CBC) and disconnected projections redundancy compensation technique (DIRECT). First the theory and analytical model of the cardiac temporal resolution is outlined. Next, the performance of the proposed algorithms is evaluated by using computer simulations as well as patient data. It will be shown that the proposed algorithms enhance the robustness of the image quality against inconsistencies by guaranteeing smooth transition of heart cycles used in reconstruction.

Towards an inline reconstruction architecture for micro-CT systems

Recent developments in micro-CT have revolutionized the ability to examine in vivo living experimental animal models such as mouse with a spatial resolution less than 50 microm. The main requirements of in vivo imaging for biological researchers are a good spatial resolution, a low dose induced to the animal during the full examination and a reduced acquisition and reconstruction time for screening purposes. We introduce inline acquisition and reconstruction architecture to obtain in real time the 3D attenuation map of the animal fulfilling the three previous requirements. The micro-CT system is based on commercially available x-ray detector and micro-focus x-ray source. The reconstruction architecture is based on a cluster of PCs where a dedicated communication scheme combining serial and parallel treatments is implemented. In order to obtain high performance transmission rate between the detector and the reconstruction architecture, a dedicated data acquisition system is also developed. With the proposed solution, the time required to filter and backproject a projection of 2048 x 2048 pixels inside a volume of 140 mega voxels using the Feldkamp algorithm is similar to 500 ms, the time needed to acquire the same projection.

Helical cone beam CT with an asymmetrical detector

If a multislice or other area detector is shifted to one side to cover a larger field of view, then the data are truncated on one side. We propose a method to restore the missing data in helical cone-beam acquisitions that uses measured data on the longer side of the asymmetric detector array. The method is based on the idea of complementary rays, which is well known in fan beam geometry; in this paper we extend this concept to the cone-beam case. Different cases of complementary data coverage and dependence on the helical pitch are considered. The proposed method is used in our prototype 16-row CT scanner with an asymmetric detector and a 700 mm field of view. For evaluation we used scanned body phantom data and computer-simulated data. To simulate asymmetric truncation, the full, symmetric datasets were truncated by dropping either 22.5% or 45% from one side of the detector. Reconstructed images from the prototype scanner with the asymmetrical detector show excellent image quality in the extended field of view. The proposed method allows flexible helical pitch selection and can be used with overscan, short-scan, and super-short-scan reconstructions.

An approximate short scan helical FDK cone beam algorithm based on nutating curved surfaces satisfying the Tuy's condition

Traditionally, short scan helical FDK algorithms have been implemented based on horizontal transaxial slices. However, not every point on the horizontal transaxial slice satisfies Tuy's condition for the corresponding (pi+fan angle) segment of helix, which means that some points on the horizontal slices are incompletely sampled and are impossible to be exactly reconstructed. In this paper, we propose and implement an improved but still approximate short scan helical cone beam FDK algorithm based on nutating curved surfaces satisfying the Tuy's condition. This surface is defined by averaging PI surfaces emanating the initial and final source points of a (pi+fan angle) segment of helix. One of the key characteristics of the surface is that every point on it satisfies the Tuy's condition for the corresponding (pi+fan angle) segment of helix, which means that we can potentially reconstruct every point on the surface exactly. This difference makes the proposed algorithm deliver a better-reconstructed image quality while requiring a smaller detector area than that of traditional FDK methods based on horizontal transaxial slices. Another characteristic of the proposed surface is that every point within the helix belongs to one and only one such surface. Therefore, the location of the short scan segment for the reconstruction of a point in Cartesian coordinate could be precalculated and stored in a look-up table. This enables us to perform reconstruction directly on rectangular grids. We compare the performance of the improved FDK algorithm with that of a quasi-exact algorithm based on data combination technique. The simulation results show that the reconstructed image quality of these two methods is similar.

Image reconstruction for the circle-and-arc trajectory

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