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In this paper, we consider 3D tomographic reconstruction for axially symmetric objects from a single radiograph formed by cone-beam X-rays. All contemporary density reconstruction methods in high-energy X-ray radiography are based on the assumption that the cone beam can be treated as fan beams located at parallel planes perpendicular to the symmetric axis, so that the density of the whole object can be recovered layer by layer. Considering the relationship between different layers, we undertake the cone-beam global reconstruction to solve the ambiguity effect at the material interfaces of the reconstruction results. In view of the anisotropy of classical discrete total variations, a new discretization of total variation which yields sharp edges and has better isotropy is introduced in our reconstruction model. Furthermore, considering that the object density consists of continually changing parts and jumps, a high-order regularization term is introduced. The final hybrid regularization model is solved using the alternating proximal gradient method, which was recently applied in image processing. Density reconstruction results are presented for simulated radiographs, which shows that the proposed method has led to an improvement in terms of the preservation of edge location.

International audience; For situations of cone-beam scanning where the measurements are incomplete, we propose a method to quantify the severity of the missing information at each voxel. This incompleteness metric is geometric; it uses only the relative locations of all cone-beam vertices with respect to the voxel in question, and does not apply global information such as the object extent or the pattern of incompleteness of other voxels. The values are non-negative, with zero indicating "least incompleteness," i.e. minimal danger of incompleteness artifacts. The incompleteness value can be related to the severity of the potential reconstruction artifact at the voxel location, independent of reconstruction algorithm. We performed a computer simulation of x-ray sources along a circular trajectory, and used small multi-disk test-objects to examine the local effects of data incompleteness. The observed behavior of the reconstructed test-objects quantitatively matched the precalculated incompleteness values. A second simulation of a hypothetical SPECT breast imaging system used only 12 pinholes. Reconstructions were performed using analytic and iterative methods, and five reconstructed test-objects matched the behavior predicted by the incompleteness model. The model is based on known sufficiency conditions for data incompleteness, and provides strong predictive guidance for what can go wrong with incomplete cone-beam data.

This chapter outlines the fundamentals of several image reconstruction approaches currently in use in X-ray tomography at synchrotron radiation facilities and at industrial X-ray CT scanners, clarifying both their proper use and points of caution in image reconstruction. The chapter begins with the basic measurement methods for projection data, together with the basics of the projection data itself. Measurements with X-ray CT scanners can be thought of as a single set of Radon transforms collected while varying the projection angles. Similarly, X-ray tomography image reconstruction can be perceived as the inverse problem of analytically obtaining an object image by inverse Radon transform. Such fundamentals are described at the beginning including sinogram and the projection theorem. Various image reconstruction techniques, such as algebraic reconstruction technique, iterative reconstruction technique, filtered back projection, convolution back projection and cone beam reconstruction are then described. Especially image reconstruction methods for actual use are described in details such as on the shapes and equations of reconstruction filters in both the real space and frequency space, together with various schematic and real examples. Realities of image reconstruction are then introduced mainly on the practical applications of GPU-based image reconstruction. Finally, special image reconstructions, such as the offset scan, region of interest reconstruction, laminography and image reconstruction with angle constraints are introduced.

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

Purpose A method was developed to obtain three-dimensional (3D) point spread functions (PSFs) of reconstructed x-ray volumetric images using spheres of known diameters. The algorithm consists of a sphere localization step using template matching applied to the entire volume. Richardson Lucy (RL) deconvolution is used atypically to determine the PSF from the reconstructed x-ray image and a model of the sphere. The resulting PSF is arbitrary, that is, there are no assumptions of separability or symmetry. Oversampling is not used, and sample spacing matches the image. The effect of sphere radius on PSF estimate reproducibility is investigated. Methods Phantoms were constructed by suspending five polytetrafluoroethylene (PTFE) spheres having known radii equal to 4.77, 7.95, 9.52, 12.68, and 19.53 mm in an agar solution. The phantom included a 25 μm steel wire to calculate a line spread function (LSF). The phantom was imaged and reconstructed with a Medtronic surgical O-Arm 23 times and a Toshiba Aquilion One computed tomography (CT) 20 times. A sharp reconstruction kernel exhibiting a nonmonotonic PSF was used with the Toshiba CT. PSFs and LSFs were computed for all of the images and repeated estimates were used to compute mean and standard deviation values for every point of the PSFs and LSFs. The PSFs from spheres were converted to LSFs and compared to the wire LSF. Results The standard deviations of the PSF estimates exhibit a decreasing trend as the sphere radius is increased. The PSF from the smallest 4.77 mm sphere is the least reproducible. The normalized root mean square difference between the mean LSF derived from the 4.77 mm radius sphere and the mean wire LSF is 2.0% for the O-arm and 1.2% for the CT. Conclusion Richardson Lucy (RL) deconvolution provides a method to estimate generalized (no separability or other simplifying assumptions) 3D PSFs from spheres. X-ray noise in images acquired with typical clinical protocols cause noticeable variations in PSF estimates which can be mitigated by selecting larger spheres and combining PSF estimates from different images.

In this paper, we present a new deep learning framework for 3-D tomographic reconstruction. To this end, we map filtered back-projection-type algorithms to neural networks. However, the back-projection cannot be implemented as a fully connected layer due to its memory requirements. To overcome this problem, we propose a new type of cone-beam back-projection layer, efficiently calculating the forward pass. We derive this layer’s backward pass as a projection operation. Unlike most deep learning approaches for reconstruction, our new layer permits joint optimization of correction steps in volume and projection domain. Evaluation is performed numerically on a public data set in a limited angle setting showing a consistent improvement over analytical algorithms while keeping the same computational test-time complexity by design. In the region of interest, the peak signal-to-noise ratio has increased by 23%. In addition, we show that the learned algorithm can be interpreted using known concepts from cone beam reconstruction: the network is able to automatically learn strategies such as compensation weights and apodization windows.

We present a novel method which provides X-ray CT users the flexibility to reconstruct an object along any of its internal flat features. This internal feature, which is generally not parallel to the object's external surface, can be either an interface between two materials or one surface of an internal layer. This method is developed based on our existing CT differential reconstruction algorithm that is achieved by modifying the popular Feldkamp-Davis-Kress cone-beam reconstruction technique. The theory of this technology is described. One case-study demonstrates that this method is independent of the surface selection of several parallel features. Another case-study shows its capability to reconstruct any individual plate along the plate's own orientation with a three-plate object.

Purpose: The present work evaluates an iterative reconstruction approach, namely, the ordered subsets convex (OSC) algorithm with regularization via total variation (TV) minimization in the field of cone-beam optical computed tomography (optical CT). One of the uses of optical CT is gel-based 3D dosimetry for radiation therapy, where it is employed to map dose distributions in radiosensitive gels. Model-based iterative reconstruction may improve optical CT image quality and contribute to a wider use of optical CT in clinical gel dosimetry. Methods: This algorithm was evaluated using experimental data acquired by a cone-beam optical CT system, as well as complementary numerical simulations. A fast GPU implementation of OSC-TV was used to achieve reconstruction times comparable to those of conventional filtered backprojection. Images obtained via OSC-TV were compared with the corresponding filtered backprojections. Spatial resolution and uniformity phantoms were scanned and respective reconstructions were subject to evaluation of the modulation transfer function, image uniformity, and accuracy. The artifacts due to refraction and total signal loss from opaque objects were also studied. Results: The cone-beam optical CT data reconstructions showed that OSC-TV outperforms filtered backprojection in terms of image quality, thanks to a model-based simulation of the photon attenuation process. It was shown to significantly improve the image spatial resolution and reduce image noise. The accuracy of the estimation of linear attenuation coefficients remained similar to that obtained via filtered backprojection. Certain image artifacts due to opaque objects were reduced. Nevertheless, the common artifact due to the gel container walls could not be eliminated. Conclusions: The use of iterative reconstruction improves cone-beam optical CT image quality in many ways. The comparisons between OSC-TV and filtered backprojection presented in this paper demonstrate that OSC-TV can potentially improve the rendering of spatial features and reduce cone-beam optical CT artifacts.

To investigate the performance of acceleration technologies for FDK algorithm, two of the most common high-performance computing hardware, multi-core CPU and GPU, are involved in our experiment. Both runtime and accuracy are regarded as the standards to evaluate the performance of four different programming methods: OpenMP, GLSL, CUDA and OpenCL. All the methods are estimated with comparable optimization strategies. The experimental results show that GPU has higher efficiency than multi-core CPU for fast cone-beam reconstruction, meanwhile CUDA is the best choice for programming on the multi-processor featured GPU.

Over the past two decades, rapid system and hardware development of x-ray computed tomography (CT) technologies has been accompanied by equally exciting advances in image reconstruction algorithms. The algorithmic development can generally be classified into three major areas: analytical reconstruction, model-based iterative reconstruction, and application-specific reconstruction. Given the limited scope of this chapter, it is nearly impossible to cover every important development in this field; it is equally difficult to provide sufficient breadth and depth on each selected topic. As a compromise, we have decided, for a selected few topics, to provide sufficient high-level technical descriptions and to discuss their advantages and applications.

International audience; In clinical studies, high resolution peripheral quantitative computed tomography (HR-pQCT) is used to separately evaluate cortical bone and trabecular bone with an isotropic voxel of 82 µm3, and typical cortical parameters are cortical density (D.comp), thickness (Ct.Th), and porosity (Ct.Po).In vitro, micro-computed tomography (micro-CT) is used to explore the internal cortical bone micro-structure with isotropic voxels and high resolution synchrotron radiation (SR); micro-CT is considered the 'gold standard'.In 16 tibias and 8 femurs, HR-pQCT measurements were compared to conventional micro-CT measurements. To test modality effects, conventional micro-CT measurements were compared to SR micro-CT measurements at 7.5 µm3; SR micro-CT measurements were also tested at different voxel sizes for the femurs, specifically, 7.5 µm3 versus 2.8 µm3.D.comp (r = −0.88, p

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.

The present work is concerned with the evaluation of the performance and the efficient implementation of multiplicative algebraic reconstruction technique (MART) to reconstruct three-dimensional (3D) objects for two different source/detector trajectories. Three types of MART algorithms are tested on a numerical phantom (Defrise), and they are implemented on a 3D X-ray system of Vikram Sarabhai Space Centre (VSSC). Circular and helical cone-beam trajectories are used. The results are compared with convolution backprojection (CBP) algorithm for each trajectory. It is found that iterative algorithms perform better than their counterpart, the transform-based CBP algorithm, whenever tomography systems are ill-conditioned due to limited views and/or noisy projection data.

Developing an efficient tool for accurate three-dimensional imaging from projections measured with C-arm systems.A circle-plus-arc trajectory, which is complete and thus amenable to accurate reconstruction, is used. This trajectory is particularly attractive as its implementation does not require moving the patient. For reconstruction, we use the "M-line method", which allows processing the data in the efficient filtered backprojection mode. This method also offers the advantage of not requiring an ideal data acquisition geometry, i.e., the M-line algorithm can account for known deviations in the scanning geometry, which is important given that sizeable deviations are generally encountered in C-arm imaging.A robust implementation scheme of the "M-line method" that applies straightforwardly to real C-arm data is presented. In particular, a numerically stable technique to compute the view-dependent derivative with respect to the source trajectory parameter is applied, and an efficient way to compute the π-line backprojection intervals via a polygonal weighting mask is presented. Projection data of an anthropomorphic thorax phantom were acquired on a medical C-arm scanner and used to demonstrate the benefit of using a complete data acquisition geometry with an accurate reconstruction algorithm versus using a state-of-the-art implementation of the conventional Feldkamp algorithm with a circular short scan of cone-beam data. A significant image quality improvement based on visual assessment is shown in terms of cone-beam artifacts.

We propose a method for improving the quality of cone-beam tomographic reconstruction done with a C-arm. C-arm scans frequently suffer from incomplete information due to image truncation, limited scan length, or other limitations. Our proposed "hybrid reconstruction" method injects information from a prior anatomical model, derived from a subject-specific computed tomography (CT) or from a statistical database (atlas), where the C-arm X-ray data is missing. This significantly reduces reconstruction artifacts with little loss of true information from the X-ray projections. The methods consist of constructing anatomical models, fast rendering of digitally reconstructed radiograph (DRR) projections of the models, rigid or deformable registration of the model and the X-ray images, and fusion of the DRR and X-ray projections, all prior to a conventional filtered back-projection algorithm. Our experiments, conducted with a mobile image intensifier C-arm, demonstrate visually and quantitatively the contribution of data fusion to image quality, which we assess through comparison to a "ground truth" CT. Importantly, we show that a significantly improved reconstruction can be obtained from a C-arm scan as short as 90° by complementing the observed projections with DRRs of two prior models, namely an atlas and a preoperative same-patient CT. The hybrid reconstruction principles are applicable to other types of C-arms as well.

In computed tomography, the application of iterative reconstruction methods in practical situations is impeded by their high computational demands. Especially in high resolution X-ray computed tomography, where reconstruction volumes contain a high number of volume elements (several giga voxels), this computational burden prevents their actual breakthrough. Besides the large amount of calculations, iterative algorithms require the entire volume to be kept in memory during reconstruction, which quickly becomes cumbersome for large data sets. To overcome this obstacle, we present a novel multiresolution reconstruction, which greatly reduces the required amount of memory without significantly affecting the reconstructed image quality. It is shown that, combined with an efficient implementation on a graphical processing unit, the multiresolution approach enables the application of iterative algorithms in the reconstruction of large volumes at an acceptable speed using only limited resources.

The ongoing development of easily accessible, fast optical readout tools promises to remove one of the barriers to acceptance of gel dosimetry as a viable tool in cancer clinics. This paper describes the characterization of a number of basic properties of the Vista cone beam CCD-based optical scanner, which can obtain high resolution reconstructed data in less than 20 min total imaging and reconstruction time. The suitability of a filtered back projection cone beam reconstruction algorithm is established for optically absorbing dosimeters using this scanner configuration. The system was then shown to be capable of imaging an optically absorbing media-filled 1 L polyethylene terephthalate (PETE) jar dosimeter to a reconstructed voxel resolution of 0.5 x 0.5 x 0.5 mm(3). At this resolution, more than 60% of the imaged volume in the dosimeter exhibits minimal spatial distortion, a measurement accuracy of 3-4% and the mean to standard deviation signal-to-noise ratio greater than 100 over an optical absorption range of 0.06-0.18 cm(-1). An inter-day scan precision of 1% was demonstrated near the upper end of this range. Absorption measurements show evidence of stray light perturbation causing artifacts in the data, which if better managed would improve the accuracy of optical readout. Cone beam optical attenuation measurements of scattering dosimeters, on the other hand, are nonlinearly affected by angled scatter stray light. Scatter perturbation leads to significant cupping artifacts and other inaccuracies that greatly limit the readout of scattering polymer gel dosimeters with cone beam optical CT.

Noninvasive imaging of the heart using computed tomography (CT) is an increasingly important diagnostic approach for patients with known or suspected coronary artery disease. Coronary CT angiography has recently received great attention because it provides imaging of the coronary arteries and quantification of the coronary plaque burden with a spatial and temporal resolution not available with any other noninvasive imaging test. In this moderated scientific debate we discuss the advantages and disadvantages of different technical solutions to CT imaging of the fast moving heart including its small and tortuous coronary arteries. Our discussion goes into the details of developments regarding larger Z-axis coverage (320-row volume CT, high pitch spiral acquisition), improved temporal resolution (dual-source CT, adaptive multi-segment reconstruction, and shorter gantry rotation times with air-bearing gantries), improved spatial resolution (high-definition detectors), and improved reconstruction algorithms (iterative reconstruction, cone beam reconstruction). The discussion also touches on the future technological developments that will be necessary to further improve the acceptance and widespread clinical use of cardiac CT, focusing on radiation exposure reduction and independence from heart rate. Finally, the representatives of the four main vendors explain the most important research projects regarding cardiac CT that they plan to pursue in the near future.

Axial scan along circular trajectory has been the most desirable in clinical and preclinical applications. However, due to the violation of the data sufficiency condition, the reconstruction accuracy of axial scan deteriorates rapidly with increasing detector z -dimension. A number of algorithms have been proposed thus far to improve the reconstruction accuracy. It is well understood that, the larger the radius of circular trajectory, the more accurate the reconstruction. Ultimately, the reconstruction becomes accurate if the trajectory radius reaches infinite. Inspired by such observations, an asymptotic weighting scheme is proposed here for axial scan at large cone angles to improve reconstruction accuracy. In practice, there may be other ways to implement the asymptotic 3-D weighting scheme, and we present one approach in this paper with preliminary results. Further investigation may enable this asymptotic weighting scheme to improve reconstruction accuracy significantly, enabling numerous applications in which axial scan at large z -dimension is desired.

Purpose: Fast 3D cone beam reconstruction is mandatory for many clinical workflows. For that reason, researchers and industry work hard on hardware-optimized 3D reconstruction. Backprojection is a major component of many reconstruction algorithms that require a projection of each voxel onto the projection data, including data interpolation, before updating the voxel value. This step is the bottleneck of most reconstruction algorithms and the focus of optimization in recent publications. A crucial limitation, however, of these publications is that the presented results are not comparable to each other. This is mainly due to variations in data acquisitions, preprocessing, and chosen geometries and the lack of a common publicly available test dataset. The authors provide such a standardized dataset that allows for substantial comparison of hardware accelerated backprojection methods. Methods: They developed an open platform RabbitCT www.rabbitCT.com for worldwide comparison in backprojection performance and ranking on different architectures using a specific high resolution C-arm CT dataset of a rabbit. This includes a sophisticated benchmark interface, a prototype implementation in C, and image quality measures. Results: At the time of writing, six backprojection implementations are already listed on the website. Optimizations include multithreading using Intel threading building blocks and OpenMP, vectorization using SSE, and computation on the GPU using CUDA 2.0. Conclusions: There is a need for objectively comparing backprojection implementations for reconstruction algorithms. RabbitCT aims to provide a solution to this problem by offering an open platform with fair chances for all participants. The authors are looking forward to a growing community and await feedback regarding future evaluations of novel software- and hardware-based acceleration schemes. © 2009 American Association of Physicists in Medicine. DOI: 10.1118/1.3180956

Recently, 3D image fusion reconstruction using a FDK algorithm along three-orthogonal circular isocentric orbits has been proposed. On the other hand, we know that 3D image reconstruction based on three-orthogonal circular isocentric orbits is sufficient in the sense of Tuy data sufficiency condition. Therefore the datum obtained from three-orthogonal circular isocentric orbits can derive an exact reconstruction algorithm. In this paper, an exact weighted-FBP algorithm with three-orthogonal circular isocentric orbits is derived by means of Katsevich's equations of filtering lines based on a circle trajectory and a modified weighted form of Tuy's reconstruction scheme.

The purpose of this study was to use phantom and patient data acquired with 64-MDCT to compare the image quality and characteristics of helical high-resolution CT images obtained with cone-beam reconstruction with those of stepwise high-resolution CT images obtained with fan-beam reconstruction.We reconstructed helical high-resolution CT images with cone-beam technique and stepwise high-resolution CT images with fan-beam technique. In the phantom study, we measured high-contrast spatial resolution and image noise using a phantom. Streak artifact was evaluated by five radiologists using the phantom. In the clinical phase of the study, two radiologists independently evaluated high-resolution helical and stepwise CT images of the lung fields of 30 patients with diffuse lung disease. Using a 3-point ordinal scale, the radiologists assessed the sharpness of peripheral vessels and interlobular fissures, artifacts, and graininess in the lung fields; overall image quality; and the sharpness of the contour of the left ventricle.In high-contrast spatial resolution, the contrast curves in each spatial frequency were similar on the helical and stepwise images. In the clinical study, there was no statistically significant difference between helical and stepwise images with respect to sharpness of the contour of the left ventricle, peripheral vessels, or interlobular fissures (p0.05). With respect to streak artifacts and graininess in the lung fields, helical images received a significantly higher quality grade than did stepwise images (p0.05).Our phantom and clinical evaluation showed that the quality of high-resolution CT images of the lung obtained with helical scanning was comparable with the quality of stepwise scans.

Use of cone-beam computed tomography (CBCT) is becoming more frequent. For proper reconstruction, the geometry of the CBCT systems must be known. While the system can be designed to reduce errors in the geometry, calibration measurements must still be performed and corrections applied. Investigators have proposed techniques using calibration objects for system calibration. In this study, the authors present methods to calibrate a rotary-stage CB micro-CT (CBμCT) system using only the images acquired of the object to be reconstructed, i.e., without the use of calibration objects. Projection images are acquired using a CBμCT system constructed in the authors’ laboratories. Dark- and flat-field corrections are performed. Exposure variations are detected and quantified using analysis of image regions with an unobstructed view of the x-ray source. Translations that occur during the acquisition in the horizontal direction are detected, quantified, and corrected based on sinogram analysis. The axis of rotation is determined using registration of antiposed projection images. These techniques were evaluated using data obtained with calibration objects and phantoms. The physical geometric axis of rotation is determined and aligned with the rotational axis (assumed to be the center of the detector plane) used in the reconstruction process. The parameters describing this axis agree to within 0.1 mm and 0.3 deg with those determined using other techniques. Blurring due to residual calibration errors has a point-spread function in the reconstructed planes with a full-width-at-half-maximum of less than 125 μm in a tangential direction and essentially zero in the radial direction for the rotating object. The authors have used this approach on over 100 acquisitions over the past 2 years and have regularly obtained high-quality reconstructions, i.e., without artifacts and no detectable blurring of the reconstructed objects. This self-calibrating approach not only obviates calibration runs, but it also provides quality control data for each data set.

State-of-the-art filtered backprojection (FBP) algorithms often define the filtering operation to be performed along oblique filtering lines in the detector. A limited scan field of view leads to the truncation of those filtering lines, which causes artifacts in the final reconstructed volume. In contrast to the case where filtering is performed solely along the detector rows, no methods are available for the case of oblique filtering lines. In this work, the authors present two novel truncation correction methods which effectively handle data truncation in this case. Method 1 (basic approach) handles data truncation in two successive preprocessing steps by applying a hybrid data extrapolation method, which is a combination of a water cylinder extrapolation and a Gaussian extrapolation. It is independent of any specific reconstruction algorithm. Method 2 (kink approach) uses similar concepts for data extrapolation as the basic approach but needs to be integrated into the reconstruction algorithm. Experiments are presented from simulated data of the FORBILD head phantom, acquired along a partial-circle-plus-arc trajectory. The theoretically exact M-line algorithm is used for reconstruction. Although the discussion is focused on theoretically exact algorithms, the proposed truncation correction methods can be applied to any FBP algorithm that exposes oblique filtering lines.

Since coronary heart disease is one of the main causes of death all over the world, cardiac computed tomography (CT) imaging is an application of very high interest in order to verify indications timely. Due to the cardiac motion, electrocardiogram (ECG) gating has to be implemented into the reconstruction of the measured projection data. However, the temporal and spatial resolution is limited due to the mechanical movement of the gantry and due to the fact that a finite angular span of projections has to be acquired for the reconstruction of each voxel. In this article, a motion-compensated reconstruction method for cardiac CT is described, which can be used to increase the signal-to-noise ratio or to suppress motion blurring. Alternatively, it can be translated into an improvement of the temporal and spatial resolution. It can be applied to the entire heart in common and to high contrast objects moving with the heart in particular, such as calcified plaques or devices like stents. The method is based on three subsequent steps: As a first step, the projection data acquired in low pitch helical acquisition mode together with the ECG are reconstructed at multiple phase points. As a second step, the motion-vector fieldmore » is calculated from the reconstructed images in relation to the image in a reference phase. Finally, a motion-compensated reconstruction is carried out for the reference phase using those projections, which cover the cardiac phases for which the motion-vector field has been determined.« less

We have developed a new four-dimensional cone beam CT (4D-CBCT) on a Varian image-guided radiation therapy system, which has radiation therapy treatment and cone beam CT imaging capabilities. We adapted the speed of gantry rotation time of the CBCT to the average breath cycle of the patient to maintain the same level of image quality and adjusted the data sampling frequency to keep a similar level of radiation exposure to the patient. Our design utilized the real-time positioning and monitoring system to record the respiratory signal of the patient during the acquisition of the CBCT data. We used the full-fan bowtie filter during data acquisition, acquired the projection data over 200 deg of gantry rotation, and reconstructed the images with a half-scan cone beam reconstruction. The scan time for a 200-deg gantry rotation per patient ranged from 3.3 to 6.6 min for the average breath cycle of 3-6 s. The radiation dose of the 4D-CBCT was about 1-2 times the radiation dose of the 4D-CT on a multislice CT scanner. We evaluated the 4D-CBCT in scanning, data processing and image quality with phantom studies. We demonstrated the clinical applicability of the 4D-CBCT and compared the 4D-CBCT and the 4D-CT scans in four patient studies. The contrast-to-noise ratio of the 4D-CT was 2.8-3.5 times of the contrast-to-noise ratio of the 4D-CBCT in the four patient studies.

A cone-angle-based window function is defined in this manuscript for image reconstruction using helical cone beam filtered backprojection (CB-FBP) algorithms. Rather than defining the window boundaries in a two-dimensional detector acquiring projection data for computed tomographic imaging, the cone-angle-based window function deals with data redundancy by selecting rays with the smallest cone angle relative to the reconstruction plane. To be computationally efficient, an asymptotic approximation of the cone-angle-based window function is also given and analyzed in this paper. The benefit of using such an asymptotic approximation also includes the avoidance of functional discontinuities that cause artifacts in reconstructed tomographic images. The cone-angle-based window function and its asymptotic approximation provide a way, equivalent to the Tam-Danielsson-window, for helical CB-FBP reconstruction algorithms to deal with data redundancy, regardless of where the helical pitch is constant or dynamically variable during a scan. By taking the cone-parallel geometry as an example, a computer simulation study is conducted to evaluate the proposed window function and its asymptotic approximation for helical CB-FBP reconstruction algorithm to handle data redundancy. The computer simulated Forbild head and thorax phantoms are utilized in the performance evaluation, showing that the proposed cone-angle-based window function and its asymptotic approximation can deal with data redundancy very well in cone beam image reconstruction from projection data acquired along helical source trajectories. Moreover, a numerical study carried out in this paper reveals that the proposed cone-angle-based window function is actually equivalent to the Tam-Danielsson-window, and rigorous mathematical proofs are being investigated.

The objective of this study was to introduce the technical utility of micro-computed tomography (CT) with 27-mum resolution by cone-beam CT algorithm. Whole-body micro-CT scans were performed to honeybee. Two- and three-dimensional image analyses were performed by originally developed and available open-source software for acquired images. The original contribution of this work is to describe the technical characteristics of the X-ray micro-CT system, keeping a small experimental insect in a unique condition. Micro-CT may be used as a rapid prototyping tool to research and understand the high-resolution system with Feldkamp cone-beam reconstruction.

Digital breast tomosynthesis (DBT) provides 3D images which remove tissue overlapping and enables better cancer detection. Stationary DBT (s-DBT) uses a fixed X-ray source array to eliminate image blur associated with the x-ray tube motion and provides better image quality as well as faster scanning speed. For limited angle tomography, it is known that iterative reconstructions generally produces better images with fewer artifacts. However classical iterative tomosynthesis reconstruction methods are considerably slower than the filtered back-projection (FBP) reconstruction. The linear x-ray source array used in s-DBT enables a computationally more efficient volume reconstruction using adapted fan beam slice sampling, which transforms the 3-D cone beam reconstruction to a series of 2-D fan beam slice reconstructions. In this paper, we report the first results of the adapted fan-beam volume reconstruction (AFVR) for the s-DBT system currently undergoing clinical trial at UNC, using a simultaneous algebraic reconstruction technique (SART). An analytic breast phantom is used to quantitatively analyze the performance of the AFVR. Image quality of a CIRS biopsy phantom reconstructed using the AFVR method are compared to that using FBP algorithm with a commercial package. Our results show a significant reduction in memory usage and an order of magnitude speed increase in reconstructing speed using AFVR compared to that of classical 3-D cone beam reconstruction. We also observed that images reconstructed by AFVR with SART had a better sharpness and contrast compared to that using FBP. Preliminary results on patient images demonstrates the improved detectability of the s-DBT system over the mammography. By utilizing parallel computing with graphics processing unit (GPU), it is expected that the AFVR method will enable iterative reconstruction technique to be practical for clinical applications.

Cone beam computed tomography (CBCT) systems with rotational gantries that have standard flat panel detectors (FPD) are widely used for the 3D rendering of vascular structures using Feldkamp cone beam reconstruction algorithms. One of the inherent limitations of these systems is limited resolution (

Computed tomography requires the solution of an inverse problem, that is, the reconstruction of an object distribution from measurement data. In hard field tomography this problem can be more specifically referred to as the reconstruction of an object distribution from its line integrals. A first solution to the mathematical problem was given by Johann Radon in 1917 long before anyone thought about computed tomography. The transformation of an object distribution into the space of its line integrals is hence today called the Radon transformation. With the later development of computed tomography technology, quite powerful algorithms based on analytic and algebraic inversion schemes for the Radon transformation were developed. This chapter introduces the mathematical fundamentals of the forward and inverse problem of hard field computed tomography and the discretization of the problem and further discusses some distinct features and specialties of image reconstruction, such as three-dimensional inversion approaches and concepts for limited and local tomography.

Computed tomography (CT) is a widely used medical technology. Adding 3D imaging to a mobile fluoroscopic C-arm reduces the cost of CT, as a mobile C-arm is much less expensive than a dedicated CT scanner. In this paper we explore the technical challenges to implementing 3D reconstruction on these devices. One of the biggest challenges is the problem of uncertain geometry; mobile C-arms do not have the same geometric consistency that exists in larger dedicated CT scanners. The geometric parameters of an acquisition scan are therefore uncertain, and a naive reconstruction with these incorrect parameters leads to poor image quality. Our proposed method reconstructs the 3D image using the expectation maximization (EM) framework while jointly estimating the true geometry, thereby improving the feasibility of 3D imaging on mobile C-arms.

By reformulating Grangeat's algorithm for the circular orbit, it is discovered that an arbitrary function to be reconstructed, f(), can be expressed as the sum of three terms:f()=fMO()+fMI()+f N() wherefMO() corresponds to the Feldkamp reconstruction,fMI() represents the information derivable from the circular scan but not utilized in Feldkamp's algorithm, andfN() represents the information which cannot be derived from the circular scanning geometry. Thus, a new cone-beam reconstruction algorithm for the circular orbit is proposed as follows: (1) compute fMO() using Feldkamp's algorithm, (2) compute fMI() using the formula developed in this paper, and (3) estimatefN() using a priori knowledge such as that suggested in Grangeat's algorithm. This study shows that by including the fMI() term, the new algorithm provides more accurate reconstructions than those of Feldkamp even without thefN() estimation.

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.

Digital tomosynthesis mammography (DTM) is a promising new modality for breast cancer detection. In DTM, projection-view images are acquired at a limited number of angles over a limited angular range and the imaged volume is reconstructed from the two-dimensional projections, thus providing three-dimensional structural information of the breast tissue. In this work, we investigated three representative reconstruction methods for this limited-angle cone-beam tomographic problem, including the backprojection (BP) method, the simultaneous algebraic reconstruction technique (SART) and the maximum likelihood method with the convex algorithm (ML-convex). The SART and ML-convex methods were both initialized with BP results to achieve efficient reconstruction. A second generation GE prototype tomosynthesis mammography system with a stationary digital detector was used for image acquisition. Projection-view images were acquired from 21 angles in 3 degrees increments over a +/- 30 degrees angular range. We used an American College of Radiology phantom and designed three additional phantoms to evaluate the image quality and reconstruction artifacts. In addition to visual comparison of the reconstructed images of different phantom sets, we employed the contrast-to-noise ratio (CNR), a line profile of features, an artifact spread function (ASF), a relative noise power spectrum (NPS), and a line object spread function (LOSF) to quantitatively evaluate the reconstruction results. It was found that for the phantoms with homogeneous background, the BP method resulted in less noisy tomosynthesized images and higher CNR values for masses than the SART and ML-convex methods. However, the two iterative methods provided greater contrast enhancement for both masses and calcification, sharper LOSF, and reduced interplane blurring and artifacts with better ASF behaviors for masses. For a contrast-detail phantom with heterogeneous tissue-mimicking background, the BP method had strong blurring artifacts along the x-ray source motion direction that obscured the contrast-detail objects, while the other two methods can remove the superimposed breast structures and significantly improve object conspicuity. With a properly selected relaxation parameter, the SART method with one iteration can provide tomosynthesized images comparable to those obtained from the ML-convex method with seven iterations, when BP results were used as initialization for both methods.

This paper offers a realistic review of kilovoltage X-ray cone beam tomography integrated with the treatment machine for image-guided radiotherapy in the light of experience taking a commercial system from prototype development into clinical use. It shows that key practicalities cannot be ignored, in particular the regular characterization of mechanical flex during gantry rotation, the mapping of defects in flat panel image transducers and their response to X-ray exposure. The number of X-ray projections and the doses required for clinically useful cone beam reconstruction at different therapy sites are considered in the context of imaging that is fit for purpose. Three roles for cone beam tomography in radiotherapy are identified: patient setup in three dimensions (3D), where even low dose cone beam tissue detail is superior to megavoltage imaging; disease targeting where, despite wide field scatter and slow scanning, it is possible to generate images that are suitable for tumour delineation even at challenging sites; adaptive treatment planning, where calibrated cone beam images have been shown to provide sufficient target detail to support "plan of the day" selection and have the potential for planning with bulk corrections. With frequent use in mind, the need to limit patient dose during setup, yet maximize much needed image quality in the target zone, is considered. Finally, it is noted that the development of cone beam tomography for radiotherapy is far from complete, with X-ray source, image transducer, reconstruction algorithms and techniques for image profile collection still being researched.

— A mobile isocentric C-arm kilovoltage imager has been evaluated as a potential tool for image-guided radiotherapy. The C-arm is equipped with an amorphous silicon flat panel for high-quality image acquisition. Additionally, the device is capable of cone beam computed tomography (CT) and volumetric reconstruction. This is achieved through the application of a modified Feldkamp algorithm with acquisition over a 180° scan arc. The number of projections can be varied from 100 to 1000, resulting in a reconstructed volume 20 cm in diameter by 15-cm long. While acquisition time depends upon number of projections, acceptable quality images can be obtained in less than 60 seconds. Image resolution and contrast of cone-beam phantom images have been compared with images from a conventional CT scanner. The system has a spatial resolution of ≥ 10 lp/cm and resolution is approximately equal in all 3 dimensions. Conversely, subject contrast is poorer than conventional CT, compromised by the increased scatter and underlying noise inherent in cone beam reconstruction, as well as the absence of filtering prior to reconstruction. The mobility of the C-arm makes it necessary to determine the C-arm position relative to the linear accelerator isocenter. Two solutions have been investigated: (1) the use of fiducial markers, embedded in the linac couch, that can subsequently be registered in the image sets; and (2), a navigation approach for infrared tracking of the C-arm relative to the linac isocenter. Observed accuracy in phantom positioning ranged from 1.0 to 1.5 mm using the navigation approach and 1.5 to 2.5 mm using the fiducial-based approach. As part of this work, the impact of respiratory motion on cone-beam image quality was evaluated, and a scheme for retrospective gating was devised. Results demonstrated that kilovoltage cone beam CT provides spatial integrity and resolution comparable to conventional CT. Cone-beam CT studies of patients undergoing radiotherapy have demonstrated acceptable soft tissue contrast, allowing assessment of daily changes in target anatomy. Of the 2 approaches developed to register images to the linac isocenter, the navigation method demonstrated superior accuracy for daily patient positioning relative to the fiducial-based method. Finally, significant image degradation due to respiratory motion was observed. It was demonstrated that this could be improved by correlating the acquisition of individual 2D projections with respiration for retrospective reconstruction of phase-based volumetric datasets.

In this paper, we present concise proofs of several recently developed exact cone-beam reconstruction methods in the Tuy inversion framework, including both filtered-backprojection and backprojection-filtration formulas in the cases of standard spiral, nonstandard spiral, and more general scanning loci. While a similar proof of the Katsevich formula was previously reported, we present a new proof of the Zou and Pan backprojection-filtration formula. Our proof combines both odd and even data extensions so that only the cone-beam transform itself is utilized in the backprojection-filtration inversion. More importantly, our formulation is valid for general smooth scanning curves, in agreement with an earlier paper from our group [Ye, Zhao, Yu, and Wang, Proc. SPIE 5535, 293-300 (Aug. 6 2004)]. As a consequence of that proof, we obtain a new inversion formula, which is in a two-dimensional filtering backprojection format. A possibility for generalization of the Katsevich filtered-backprojection reconstruction method is also discussed from the viewpoint of this framework.

In this paper, three exact formulae are derived for cone-beam reconstruction with source positions on a curve or set of curves. For reconstruction at a single point, these formulae all operate by applying a filtration step followed by a backprojection step to cone-beam data. The filtering is performed along a 1D curve which is defined as the intersection of the detector surface with a filtering plane. Two of these formulae allow a flexibility in the choice of the filtering direction. In some cases, this flexibility allows the efficiency of volume reconstruction to be improved. Alternatively, the flexibility can be used to reduce the detector size necessary to avoid truncation artefacts in the reconstruction or to change the noise properties of the reconstruction.

Retrospectively gated cardiac volume CT imaging has become feasible with the introduction of heart rate adaptive cardiac CT reconstruction algorithms. The development in detector technology and the rapid introduction of multi-row detectors has demanded reconstruction schemes which account for the cone geometry. With the extended cardiac reconstruction (ECR) framework, the idea of approximate helical cone beam CT has been extended to be used with retrospective gating, enabling heart rate adaptive cardiac cone beam reconstruction. In this contribution, the ECR technique is evaluated for systems with an increased number of detector rows, which leads to larger cone angles. A simulation study has been carried out based on a 4D cardiac phantom consisting of a thorax model and a dynamic heart insert. Images have been reconstructed for different detector set-ups. Reconstruction assessment functions have been calculated for the detector set-ups employing different rotation times, relative pitches and heart rates. With the increased volume coverage of large area detector systems, low-pitch scans become feasible without resulting in extensive scan times, inhibiting single breath hold acquisitions. ECR delivers promising image results when being applied to systems with larger cone angles.

This paper describes a flexible new methodology for accurate cone beam reconstruction with source positions on a curve (or set of curves). The inversion formulas employed by this methodology are based on first backprojecting a simple derivative in the projection space and then applying a Hilbert transform inversion in the image space. The local nature of the projection space filtering distinguishes this approach from conventional filtered-backprojection methods. This characteristic together with a degree of flexibility in choosing the direction of the Hilbert transform used for inversion offers two important features for the design of data acquisition geometries and reconstruction algorithms. First, the size of the detector necessary to acquire sufficient data for accurate reconstruction of a given region is often smaller than that required by previously documented approaches. In other words, more data truncation is allowed. Second, redundant data can be incorporated for the purpose of noise reduction. The validity of the inversion formulas along with the application of these two properties are illustrated with reconstructions from computer simulated data. In particular, in the helical cone beam geometry, it is shown that 1) intermittent transaxial truncation has no effect on the reconstruction in a central region which means that wider patients can be accommodated on existing scanners, and more importantly that radiation exposure can be reduced for region of interest imaging and 2) at maximum pitch the data outside the Tam-Danielsson window can be used to reduce image noise and thereby improve dose utilization. Furthermore, the degree of axial truncation tolerated by our approach for saddle trajectories is shown to be larger than that of previous methods.

The recent improvements in CT detector and gantry technology in combination with new heart rate adaptive cone beam reconstruction algorithms enable the visualization of the heart in three dimensions at high spatial resolution. However, the finite temporal resolution still impedes the artifact-free reconstruction of the heart at any arbitrary phase of the cardiac cycle. Cardiac phases must be found during which the heart is quasistationary to obtain outmost image quality. It is challenging to find these phases due to intercycle and patient-to-patient variability. Electrocardiogram (ECG) information does not always represent the heart motion with an adequate accuracy. In this publication, a simple and efficient image-based technique is introduced which is able to deliver stable cardiac phases in an automatic and patient-specific way. From low-resolution four-dimensional data sets, the most stable phases are derived by calculating the object similarity between subsequent phases in the cardiac cycle. Patient-specific information about the object motion can be determined and resolved spatially. This information is used to perform optimized high-resolution reconstructions at phases of little motion. Results based on a simulation study and three real patient data sets are presented. The projection data were generated using a 16-slice cone beam CT system in low-pitch helical mode with parallel ECG recording.

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 approximate method for the utilization of redundant data in helical cone-beam CT is presented. It is based on the observation that the original WEDGE method provides excellent image quality if only little more than 180 degrees data are used for back-projection, and that significant low-frequency artifacts appear if a larger amount of redundant data are used. This degradation is compensated by the frequency split method: The low-frequency part of the image is reconstructed using little more than 180 degrees of data, while the high frequency part is reconstructed using all data. The resulting algorithm shows no cone-beam artifacts in a simulation of a 64-row scanner. It is further shown that the frequency split method hardly degrades the signal-to-noise ratio of the reconstructed images and that it behaves robustly in the presence of motion.

The histomorphometric analysis is based on stereologic concepts and was originally applied to biologic samples. This technique has been used to evaluate different complex structures such as ceramic filters, net structures and cancellous objects that are objects with inner connected structures. The measured histomorphometric parameters of structure are: sample volume to total reconstructed volume (BV/TV), sample surface to sample volume (BS/BV), connection thickness (Tb Th ), connection number (Tb N ) and connection separation (Tb Sp ). The anisotropy was evaluated as well. These parameters constitute the base of histomorphometric analysis. The quantification is realized over cross-sections recovered by cone beam reconstruction, where a real-time microfocus radiographic system is used as tomographic system. The three-dimensional (3D) histomorphometry, obtained from tomography, corresponds to an evolution of conventional method that is based on 2D analysis. It is more coherent with morphologic and topologic context of the sample. This work shows result from 3D histomorphometric quantification to characterize objects examined by 3D computer tomography. The results, which characterizes the internal structures of ceramic foams with different porous density, are compared to results from conventional methods.