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Ge Wang - One of the best experts on this subject based on the ideXlab platform.
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Half-scan Cone-Beam X-ray microtomography formula
Scanning, 2008Co-Authors: Ge Wang, T. H. Lin, Y. Liu, Pingchin ChengAbstract:An x-ray shadow projection microtomographic system using a scannable point source is under development at AMIL-ARTS, SUNY at Buffalo. To overcome the limitations of the commonly used Feldkamp's Cone-Beam Reconstruction formula, we have developed a generalized Feldkamp-type Cone-Beam Reconstruction formula. In the generalized Feldkamp-type Cone-Beam Reconstruction, a scanning locus can be either planar or helix-like, and a transaxial slice is reconstructed using projection data collected from a 360 degrees angular range (full scan). In this paper, the full-scan Cone-Beam formula is modified to require only projection data of approximate 180 degrees plus two fan-angles (half scan). First, a half-scan derivative-free noncircular fan-Beam Reconstruction formula is formulated. Then, a half-scan Cone-Beam Reconstruction formula is derived as an extension of the half-scan fan-Beam Reconstruction formula using Feldkamp's procedure. Typical numerical simulation results are given for both half-scan formulae. Compared with the full-scan Cone-Beam formula, the half-scan Cone-Beam formula reduces the involved angular range of projection data and allows better longitudinal/temporal resolution.
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Numerical studies on Palamodov and Generalized Feldkamp algorithm for general Cone-Beam scanning
Journal of X-ray Science and Technology, 2007Co-Authors: Kai Zeng, Er-wei Bai, Ge WangAbstract:Recently, the Palamodov algorithm, which was formulated for exact Cone-Beam Reconstruction from data collected along a continuous locus, has been proven to be an excellent approximate algorithm for general Cone Beam Reconstruction. The filtration-backprojection framework of the Palamodov algorithm is efficient for sequential and parallel implementation because its filtration step only involves a 1-D shift-invariant filtering along the tangent direction of the scanning trajectory. On the other hand, the generalized Feldkamp algorithm proposed by Wang et al. also allows approximate general Cone Beam Reconstruction. In this paper, we report a numerical study comparing these two approximate methods for the cases of helical and saddle curves. In this study, the image quality is evaluated in terms of mean square error (MSE), modulation transform function (MTF), etc. The results demonstrate that the Palamodov algorithm consistently performs similar or better than the generalized Feldkamp algorithm.
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Studies on Palamodov's algorithm for Cone-Beam CT along a general curve
Inverse Problems, 2006Co-Authors: Shiying Zhao, Ge WangAbstract:Inspired by Katsevich's exact helical Cone-Beam formula, Palamodov made the first attempt to perform exact image Reconstruction from Cone-Beam data collected along a general scanning trajectory [1]. In contrast to the well-known general exact Cone-Beam Reconstruction schemes formulated by Tuy, Smith, Grangeat and Katsevich, respectively, Palamodov's algorithm was intended to work with truncated data and without the need to specify any weighting function. In this paper, after reformulating Palamodov's formula and comparing it with Katsevich's helical Cone-Beam formula, we find that Palamodov's algorithm is not theoretically exact due to an inaccurate estimate. Then, we numerically implement it using a planar detector array and simulate the case of Cone-Beam CT with a nonstandard saddle curve as the scanning trajectory. The Reconstruction results suggest that Palamodov's algorithm is an attractive algorithm for approximate Cone-Beam Reconstruction in the case of general Cone-Beam scanning.
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A unified framework for exact Cone-Beam Reconstruction formulas.
Medical physics, 2005Co-Authors: Shiying Zhao, Ge WangAbstract: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.
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Cone-Beam X-ray tomography using continuous wavelet transformation
Wavelet Applications in Signal and Image Processing VIII, 2000Co-Authors: Shiying Zhao, Ge WangAbstract:Recently, medical computed tomography (CT) began a transition from fan-Beam to Cone-Beam geometry with the introduction of multi-row-detector systems. Therefore, Cone- Beam techniques become important for medical CT. Despite recent advances, the approximate Reconstruction method of Feldkamp remains the most commonly employed Cone-Beam Reconstruction algorithm because of its computational efficiency and clinical applicability. Unfortunately, the derivation of the Feldkamp Cone-Beam Reconstruction formula is based on geometric tilted fan neuristic. In this paper, we given a wavelet derivation of the Feldkamp Cone-Beam Reconstruction method. It is found that the Feldkamp algorithm is an outcome of a zero-order approximation to the longitudinal wavelet decomposition of the object function to be reconstructed. Since the approximation is explicitly given, error estimates can be derived analytically. Theoretically, it also arises the possibility of improvement of the Feldkamp Cone-Beam algorithm.
Roland Proksa - One of the best experts on this subject based on the ideXlab platform.
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The frequency split method for helical Cone-Beam Reconstruction.
Medical physics, 2004Co-Authors: Gilad Shechter, Th. Kohler, Ami Altman, Roland ProksaAbstract: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° 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° 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.
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Helical cardiac Cone Beam Reconstruction using retrospective ECG gating.
Physics in medicine and biology, 2003Co-Authors: Michael Grass, Robert Manzke, Tim Nielsen, Peter Koken, Roland Proksa, M Natanzon, Gilad ShechterAbstract:In modern computer tomography (CT) systems, the fast rotating gantry and the increased detector width enable 3D imaging of the heart. Cardiac volume CT has a high potential for non-invasive coronary angiography with high spatial resolution and short scan time. Due to the increased detector width, true Cone Beam Reconstruction methods are needed instead of adapted 2D Reconstruction schemes. In this paper, the extended cardiac Reconstruction method is introduced. It integrates the idea of retrospectively gated cardiac Reconstruction for helical data acquisition into a Cone Beam Reconstruction framework. It leads to an efficient and flexible algorithmic scheme for the Reconstruction of single- and multi-phase cardiac volume datasets. The method automatically adapts the number of cardiac cycles used for the Reconstruction. The Cone Beam geometry is fully taken into account during the Reconstruction process. Within this paper, results are presented on patient datasets which have been acquired using a 16-slice Cone Beam CT system.
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Angular weighted hybrid Cone-Beam CT Reconstruction for circular trajectories.
Physics in Medicine and Biology, 2001Co-Authors: M. Grass, Th. Kohler, Roland ProksaAbstract:Hybrid Reconstruction techniques have been introduced for the volume Reconstruction of axially truncated Cone-Beam computed tomography projection data acquired along a circular source-detector trajectory. The introduction of weighted half-scan techniques into this framework is described in this paper. Due to the Cone-Beam geometry it is not possible to perform the weighting on the projections as is typically done in conventional single-line computed tomography. Hence, in this paper we present an efficient way to incorporate angular weighting functions, depending on the object point position, into the framework of hybrid Cone-Beam Reconstruction. Four different angular weighting functions are introduced and discussed with respect to their Cone-Beam artefact behaviour and their influence on the signal-to-noise ratio. As a result, the most effective angular weighting function for hybrid circular Cone-Beam Reconstruction is determined by means of a simulation study based on mathematical phantoms and clinical data sets. This distance-weighted angular weighting scheme yields the best results in terms of high image quality, low computational complexity and signal-to-noise variations in the Reconstruction volume.
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Weighted hybrid Cone Beam Reconstruction for circular trajectories
2000 IEEE Nuclear Science Symposium. Conference Record (Cat. No.00CH37149), 2000Co-Authors: Michael Grass, Th. Kohler, Roland ProksaAbstract:In Cone Beam computer tomography circular detector trajectories will be one of the standard for projection data acquisition. To achieve a high volume coverage when using these projection data a hybrid Cone Beam Reconstruction technique has been recently introduced. This technique combines the ideas of fan-Beam to parallel-Beam rebinning for Cone Beam geometries and a height rebinning in a rectangular virtual detector window to a simple and efficient back projection algorithm. Using this data reorganization a hybrid Reconstruction technique can be applied which is based on a combination of full-scan and half-scan Reconstruction in a cylindrical Reconstruction volume of maximum size for a given radius of the field of view. The introduction of weighted half scan techniques into this framework leads to a decreased Cone Beam artifact level while keeping the optimal ratio between the reconstructible and irradiated volume of the scanned volume.
T. H. Lin - One of the best experts on this subject based on the ideXlab platform.
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Half-scan Cone-Beam X-ray microtomography formula
Scanning, 2008Co-Authors: Ge Wang, T. H. Lin, Y. Liu, Pingchin ChengAbstract:An x-ray shadow projection microtomographic system using a scannable point source is under development at AMIL-ARTS, SUNY at Buffalo. To overcome the limitations of the commonly used Feldkamp's Cone-Beam Reconstruction formula, we have developed a generalized Feldkamp-type Cone-Beam Reconstruction formula. In the generalized Feldkamp-type Cone-Beam Reconstruction, a scanning locus can be either planar or helix-like, and a transaxial slice is reconstructed using projection data collected from a 360 degrees angular range (full scan). In this paper, the full-scan Cone-Beam formula is modified to require only projection data of approximate 180 degrees plus two fan-angles (half scan). First, a half-scan derivative-free noncircular fan-Beam Reconstruction formula is formulated. Then, a half-scan Cone-Beam Reconstruction formula is derived as an extension of the half-scan fan-Beam Reconstruction formula using Feldkamp's procedure. Typical numerical simulation results are given for both half-scan formulae. Compared with the full-scan Cone-Beam formula, the half-scan Cone-Beam formula reduces the involved angular range of projection data and allows better longitudinal/temporal resolution.
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Cone-Beam 3D image Reconstruction in x-ray microtomography
Proceedings annual meeting Electron Microscopy Society of America, 1993Co-Authors: G. Wang, T. H. Lin, D. M. Shinozaki, P.c. Cheng, H. KimAbstract:An X-ray shadow projection microscope system using a scannable point source of X-rays is under development at AMIL-ARTS, SUNY at Buffalo, USA. The point source is generated by a focussed electron Beam, which can be steered electromagnetically in a plane perpendicular to the optical axis of the microscope. A specimen is mounted on a rotatable mechanical stage for microtomography. Considering the hardware characteristics of this system and the limitations of current Cone-Beam Reconstruction algorithms, a generalized Feldkamp’s Cone-Beam image Reconstruction algorithm has been developed at our laboratories. In our Cone-Beam Reconstruction, there are mainly two kinds of scanning scanning modes: planar and helix-like. A planar scanning locus is used to handle spherical or plate-like specimens. A typical case of planar scanning loci is a circle, which is used in Feldkamp’s Cone-Beam Reconstruction. A helix-like scanning locus is used to deal with rod-shaped specimens. Without loss of generality, a locus turn of the X-ray source can be defined in cylindrical coordinates by the following equation:
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Comments on "A Cone-Beam filtered backprojection Reconstruction algorithm for cardiac single photon emission computed tomography" by G. T. Gullberg and G. L. Zeng
IEEE transactions on medical imaging, 1993Co-Authors: Ge Wang, T. H. LinAbstract:In the above-titled work by G. T. Gullberg and G. L. Zeng (ibid., vol.11, no.1, p.91-101, 1992), a fan-Beam Reconstruction formula of a noncircular scanning locus was derived and extended for half-scan Cone-Beam Reconstruction. However, the Reconstruction formula is not exact mathematically unless a necessary condition is satisfied. In this correspondence, the commenters derive this necessary condition and provide a geometrical explanation of the condition. >
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A general Cone-Beam Reconstruction algorithm
IEEE transactions on medical imaging, 1993Co-Authors: Ge Wang, T. H. Lin, P. Cheng, D. M. ShinozakiAbstract:Considering the characteristics of the X-ray microscope system being developed at SUNY at Buffalo and the limitations of available Cone-Beam Reconstruction algorithms, a general Cone-Beam Reconstruction algorithm and several special versions of it are proposed and validated by simulation. The Cone-Beam algorithm allows various scanning loci, handles Reconstruction of rod-shaped specimens which are common in practice, and facilitates near real-time Reconstruction by providing the same computational efficiency and parallelism as L.A. Feldkamp et al.'s (1984) algorithm. Although the present Cone-Beam algorithm is not exact, it consistently gives satisfactory reconstructed images. Furthermore, it has several nice properties if the scanning locus meets some conditions. First, Reconstruction within a midplane is exact using a planar scanning locus. Second, the vertical integral of a reconstructed image is equal to that of the actual image. Third, Reconstruction is exact if an actual image is independent of rotation axis coordinate z. Also, the general algorithm can uniformize and reduce z-axis artifacts, if a helix-like scanning locus is used. >
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Preliminary error analysis of the general Cone-Beam Reconstruction algorithm
Biomedical Image Processing and Three-Dimensional Microscopy, 1992Co-Authors: Ge Wang, Pingchin Cheng, T. H. Lin, D. M. ShinozakiAbstract:An x-ray microscope system for microtomography is under development at SUNY/Buffalo, New York. Considering the characteristics of the x-ray microscope system and the limitations of current Cone-Beam Reconstruction algorithms, a general Cone-Beam image Reconstruction algorithm has been developed at AMIL-ARTS. In order to study the Reconstruction error characteristics of the general Cone-Beam algorithm, a preliminary error analysis on the algorithm is performed in this paper. The most important error source in Cone-Beam Reconstruction is the theoretical precision limitation. Like many Cone-Beam Reconstruction algorithms, the general Cone-Beam algorithm is not exact in nature. Thus, an analytic Reconstruction error formula is derived which relates the error to the specimen structure and various imaging parameters. Approximately, the Reconstruction error is proportional to either the distance from a voxel to the midplane or the pitch of a helix-like scanning locus, and inversely proportional to the size of the scanning locus. The Reconstruction error also depends on the specimen structure. The faster the structure varies along the z direction, the larger the Reconstruction error will be. Specimens are modeled as stochastic fields. Typical simulation results are then depicted and discussed.
Guang-hong Chen - One of the best experts on this subject based on the ideXlab platform.
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Exact and approximate Cone-Beam Reconstruction algorithms for C-arm based Cone-Beam CT using a two-concentric-arc source trajectory
Proceedings of SPIE--the International Society for Optical Engineering, 2008Co-Authors: Ting Liang Zhuang, Brian E. Nett, Shuai Leng, Joseph Zambelli, Guang-hong ChenAbstract:In this paper, we present shift-invariant filtered backprojection (FBP) Cone-Beam image Reconstruction algorithms for a Cone-Beam CT system based on a clinical C-arm gantry. The source trajectory consists of two concentric arcs which is complete in the sense that the Tuy data sufficiency condition is satisfied. This scanning geometry is referred to here as a CC geometry (each arc is shaped like the letter "C"). The challenge for image Reconstruction for the CC geometry is that the image volume is not well populated by the familiar doubly measured (DM) lines. Thus, the well-known DM-line based image Reconstruction schemes are not appropriate for the CC geometry. Our starting point is a general Reconstruction formula developed by Pack and Noo which is not dependent on the existence of DM-lines. For a specific scanning geometry, the filtering lines must be carefully selected to satisfy the Pack-Noo condition for mathematically exact Reconstruction. The new points in this paper are summarized here. (1) A mathematically exact Cone-Beam Reconstruction algorithm was formulated for the CC geometry by utilizing the Pack-Noo image Reconstruction scheme. One drawback of the developed exact algorithm is that it does not solve the long-object problem. (2) We developed an approximate image Reconstruction algorithm by deforming the filtering lines so that the long object problem is solved while the Reconstruction accuracy is maintained. (3) In addition to numerical phantom experiments to validate the developed image Reconstruction algorithms, we also validate our algorithms using physical phantom experiments on a clinical C-arm system.
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Arc based Cone-Beam Reconstruction algorithm using an equal weighting scheme
Journal of X-ray Science and Technology, 2007Co-Authors: Brian E. Nett, Ting Liang Zhuang, Shuai Leng, Guang-hong ChenAbstract:Conventionally, the FDK algorithm is used to reconstruct images in many imaging systems where Cone-Beam projections are acquired from a single circular scanning path in a 2π angular range (full scan mode) and has been heuristically extended to a π+fan angle angular range (short-scan mode). In this paper, a new Cone-Beam Reconstruction algorithm is derived for a single arc source trajectory with an equal weighting scheme. This algorithm is derived in the Katsevich framework. Since the single arc does not satisfy Tuy's data sufficiency condition, the resulting algorithm is an approximate Reconstruction algorithm. The feature of one-dimensional (1D) shift-invariant filtering in the conventional FDK algorithm is nicely preserved. The new algorithm includes a voxel dependent backprojection step of weighted combinations of 1D Hilbert filtered data, after an initial differentiation operation. In comparing the new algorithm with the standard FDK: the new algorithm intrinsically handles full scan, short scan and super-short scan modes. Numerical simulations have been performed to validate the algorithm, and demonstrate more quantitatively correct density values when reconstructing points away from the central slice. Noise performance was assessed for both the new algorithm and the FDK algorithm using simulated Poisson noise.
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an alternative derivation of katsevich s Cone Beam Reconstruction formula
Medical Physics, 2003Co-Authors: Guang-hong ChenAbstract:In this paper an alternative derivation of Katsevich’s Cone-Beam image Reconstruction algorithm is presented. The starting point is the classical Tuy’s inversion formula. After ~i! using the hidden symmetries of the intermediate functions, ~ii! handling the redundant data by weighting them, ~iii! changing the weighted average into an integral over the source trajectory parameter, and ~iv! imposing an additional constraint on the weighting function, a filtered backprojection Reconstruction formula from Cone Beam projections is derived. The following features are emphasized in the present paper: First, the nontangential condition in Tuy’s original data sufficiency conditions has been relaxed. Second, a practical regularization scheme to handle the singularity is proposed. Third, the derivation in the Cone Beam case is in the same fashion as that in the fan-Beam case. Our final Cone-Beam Reconstruction formula is the same as the one discovered by Katsevich in his most recent paper. However, the data sufficiency conditions and the regularization scheme of singularities are different. A detailed comparison between these two methods is presented. © 2003 American Association of Physicists in Medicine. @DOI: 10.1118/1.1628413#
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An alternative derivation of Katsevich's Cone‐Beam Reconstruction formula
Medical physics, 2003Co-Authors: Guang-hong ChenAbstract:In this paper an alternative derivation of Katsevich’s Cone-Beam image Reconstruction algorithm is presented. The starting point is the classical Tuy’s inversion formula. After ~i! using the hidden symmetries of the intermediate functions, ~ii! handling the redundant data by weighting them, ~iii! changing the weighted average into an integral over the source trajectory parameter, and ~iv! imposing an additional constraint on the weighting function, a filtered backprojection Reconstruction formula from Cone Beam projections is derived. The following features are emphasized in the present paper: First, the nontangential condition in Tuy’s original data sufficiency conditions has been relaxed. Second, a practical regularization scheme to handle the singularity is proposed. Third, the derivation in the Cone Beam case is in the same fashion as that in the fan-Beam case. Our final Cone-Beam Reconstruction formula is the same as the one discovered by Katsevich in his most recent paper. However, the data sufficiency conditions and the regularization scheme of singularities are different. A detailed comparison between these two methods is presented. © 2003 American Association of Physicists in Medicine. @DOI: 10.1118/1.1628413#
Joachim Hornegger - One of the best experts on this subject based on the ideXlab platform.
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technical note rabbitct an open platform for benchmarking 3d Cone Beam Reconstruction algorithmsa
Medical Physics, 2009Co-Authors: Christopher Rohkohl, Benjamin Keck, Hannes G. Hofmann, Joachim HorneggerAbstract: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
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Technical Note: RabbitCT—an open platform for benchmarking 3D Cone‐Beam Reconstruction algorithmsa)
Medical physics, 2009Co-Authors: Christopher Rohkohl, Benjamin Keck, Hannes G. Hofmann, Joachim HorneggerAbstract: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