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filtered backprojection algorithm can outperform iterative maximum likelihood expectation-maximization algorithm

INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY 2012年第2期22卷 114-120页

作者： Zeng, Gengsheng L. Univ Utah Dept Radiol UCAIR Salt Lake City UT 84108 USA

The iterative maximum-likelihood expectation-maximization (ML-EM) algorithm is an excellent algorithm for image reconstruction and usually provides better images than the filtered backprojection (FBP) algorithm. However, a windowed FBP algorithm can outperform the ML-EM in certain occasions, when the least-squared difference from the true image, that is, the least-squared error (LSE), is used as the comparison criterion. Computer simulations were carried out for the two algorithms. For a given data set the best reconstruction (compared to the true image) from each algorithm was first obtained, and the two reconstructions are compared. The stopping iteration number of the ML-EM algorithm and the parameters of the windowed FBP algorithm were determined, so that they produced an image that was closest to the true image. However, to use the LSE criterion to compare algorithms, one must know the true image. How to select the optimal parameters when the true image is unknown is a practical open problem. For noisy Poisson projections, computer simulation results indicate that the ML-EM images are better than the regular FBP images, and the windowed FBP algorithm images are better than the ML-EM images. For the noiseless projections, the FBP algorithms outperform the ML-EM algorithm. The computer simulations reveal that the windowed FBP algorithm can provide a reconstruction that is closer to the true image than the ML-EM algorithm. (C) 2012 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 22, 114120, 2012

关键词： image reconstruction ML-EM algorithm filtered backprojection algorithm Poisson noise

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The semidiscrete filtered backprojection algorithm is optimal for tomographic inversion

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SIAM JOURNAL ON NUMERICAL ANALYSIS 2003年第3期41卷 869-892页

作者： Rieder, A Faridani, A Univ Karlsruhe Inst Wissensch Liches Rechnen & Math Modellbildun D-76128 Karlsruhe Germany Oregon State Univ Dept Math Corvallis OR 97331 USA

The filtered backprojection algorithm is probably the most often used reconstruction algorithm in two-dimensional computerized tomography. For a semidiscrete version in the parallel scanning geometry we prove optimal L-2-convergence rates for density distributions in Sobolev spaces. Additionally we show L-2-convergence without rates when the density distribution is only in L-2. The key to success is a new representation of the filtered backprojection which enables us to apply techniques from approximation theory. Our analysis provides further a modi. cation of the Shepp Logan reconstruction filter with an improved convergence behavior. Numerical experiments in the fully discrete setting reproduce the theoretical predictions.

关键词： radon transform tomography filtered backprojection algorithm reconstruction filter

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Comments on the filtered backprojection algorithm, range conditions, and the pseudoinverse solution

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IEEE TRANSACTIONS ON MEDICAL IMAGING 2001年第6期20卷 539-542页

作者： Anastasio, MA Pan, XC Clarkson, E Univ Chicago Grad Program Med Phys Dept Radiol Chicago IL 60637 USA Univ Arizona Dept Radiol Tucson AZ 85724 USA

The filtered backprojection (FBP) algorithm is widely used in computed tomography for inverting the two-dimensional Radon transform. In this paper, we analyze the processing of an inconsistent data function by the FBP algorithm (in its continuous form). Specifically, me demonstrate that an image reconstructed using the FBP algorithm can be represented as the sum of a pseudoinverse solution and a residual image generated from an inconsistent component of the measured data. This reveals that, when the original data function is in the range of the Radon transform, the image reconstructed using the FBP algorithm corresponds to the pseudoinverse solution. When the data function is inconsistent, we demonstrate that the FBP algorithm makes use of a nonorthogonal projection of the data function to the range of the Radon transform.

关键词： computed tomography filtered backprojection algorithm radon transform

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Theoretically exact filtered backprojection-type inversion algorithm for spiral CT

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SIAM JOURNAL ON APPLIED MATHEMATICS 2002年第6期62卷 2012-2026页

作者： Katsevich, A Univ Cent Florida Dept Math Orlando FL 32816 USA

Proposed is a theoretically exact formula for inversion of data obtained by a spiral computed tomography ( CT) scan with a two- dimensional detector array. The detector array is supposed to be of limited extent in the axial direction. The main property of the formula is that it can be implemented in a truly filtered backprojection fashion. First, one performs shift- invariant filtering of a derivative of the cone beam projections, and, second, the result is backprojected in order to form an image. Another property is that the formula solves the so- called long object problem. Limitations of the algorithm are discussed. Results of numerical experiments are presented.

关键词： cone beam spiral tomography theoretically exact reconstruction filtered backprojection algorithm

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Three-dimensional reconstruction of refractive index inhomogeneities in optical phase elements

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OPTICS AND LASERS IN ENGINEERING 2002年第6期38卷 373-385页

作者： Górski, W Kujawinska, M Warsaw Univ Technol Inst Micromech & Photon PL-02525 Warsaw Poland

In this paper the quantitative approach to 3D reconstruction of refractive index inhomogeneity of static phase object is presented. The method combines multidirectional phase shifting interferometry technique with tomographic reconstruction. It is aimed on testing of optical material and elements with both symmetric and non-symmetric refractive index distributions. The optimisation of the parameters used in filtered backprojection reconstruction algorithm is performed in order to maximise the overall accuracy of measurement. Experiments are performed to verify the methodology and parameters obtained from optimisation procedure. The results prove high performance of the proposed measuring procedure. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： tomographic interferometry 3D refractive index reconstruction filtered backprojection algorithm

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Revisit of the Ramp Filter

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 2015年第1期62卷 131-136页

作者： Zeng, Gengsheng L. Weber State Univ Dept Elect Engn Ogden UT 84408 USA Univ Utah Dept Radiol Salt Lake City UT 84108 USA

An important part of the filtered backprojection (FBP) algorithm is the ramp filter. This paper derives the discrete version of the ramp filter in the Fourier domain and studies the windowing effects. When a window function is used to control the noise, the image amplitude will be affected and reduced. A simple remedy is proposed to improve the image accuracy when a window function must be used.

关键词： Analytic image reconstruction filtered backprojection algorithm

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Numerical study of two-dimensional water vapor concentration and temperature distribution of combustion zones using tunable diode laser absorption tomography

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INFRARED PHYSICS & TECHNOLOGY 2015年 72卷 170-178页

作者： Xia, Huihui Xu, Zhenyu Kan, Ruifeng He, Yabai Liu, Jianguo Zhang, Guangle Chinese Acad Sci Anhui Inst Opt & Fine Mech Key Lab Environm Opt Monitoring Tech Anhui Prov Hefei 230031 Peoples R China Univ Sci & Technol China Hefei 230022 Peoples R China

The principle of gas temperature and concentration measurement based on Tunable Diode Laser Absorption Spectroscopy (TDLAS) is introduced. Combining Computed Tomography (Cr) with TDLAS, herein referred to as Tunable Diode Laser Absorption Tomography (TDLAT), reconstructs temperature and concentration distribution which are assumed as Gaussian function or paraboloid function. A pair of water absorption lines (7153.722 cm(-1) and 7153.748 cm(-1) and 7154.354 cm(-1)) is selected to measure temperature by means of two-line technique. Radon transform is used to calculate projections of different path for reconstructing temperature distribution based on filtered backprojection algorithm. With a general normalization process, water vapor concentration distribution can be obtained simultaneously. The reconstruction results agree well with the original model. In consideration of laboratory verification and experimental condition, the TDLAT data consist of 13 projection angles and 11 parallel rays at each angle is discussed in this article, obtaining distribution map with a resolution of 20 x 20. Although the reconstruction value of the edge deviates a little from the original parameters, this method achieves relatively satisfactory outcome in general. The reconstruction error roughly increases with decreasing projection angles and parallel rays, additionally, the reconstruction accuracy is more dependent on the parallel ray number at each angle than the projection angle number. Appropriate grid partition is also important in reconstruction study, the optimal grid partition is 30 x 30 or near this magnitude when the system contains totally 18 projection angles and 27 parallel rays at each angle. This work proposes a feasible formula for reconstruction research with a small amount of projections and rays, theoretically, laying a foundation for experimental validation in the future. (c) 2015 Elsevier B.V. All rights reserved.

关键词： Laser absorption spectroscopy Two-dimensional distribution filtered backprojection algorithm Projection rays Computer tomography

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Tilted cone-beam reconstruction with row-wise fan-to-parallel rebinning

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PHYSICS IN MEDICINE AND BIOLOGY 2006年第20期51卷 5259-5276页

作者： Hsieh, Jiang Tang, Xiangyang GE Co Healthcare Technol Waukesha WI 53188 USA

Reconstruction algorithms for cone-beam CT have been the focus of many studies. Several exact and approximate reconstruction algorithms were proposed for step-and-shoot and helical scanning trajectories to combat cone-beam related artefacts. In this paper, we present a new closed-form cone-beam reconstruction formula for tilted gantry data acquisition. Although several algorithms were proposed in the past to combat errors induced by the gantry tilt, none of the algorithms addresses the scenario in which the cone-beam geometry is first rebinned to a set of parallel beams prior to the filtered backprojection. We show that the image quality advantages of the rebinned parallel-beam reconstruction are significant, which makes the development of such an algorithm necessary. Because of the rebinning process, the reconstruction algorithm becomes more complex and the amount of iso-centre adjustment depends not only on the projection and tilt angles, but also on the reconstructed pixel location. In this paper, we first demonstrate the advantages of the row-wise fan-to-parallel rebinning and derive a closed-form solution for the reconstruction algorithm for the step-and-shoot and constant-pitch helical scans. The proposed algorithm requires the 'warping' of the reconstruction matrix on a view-by-view basis prior to the backprojection step. We further extend the algorithm to the variable-pitch helical scans in which the patient table travels at non-constant speeds. The algorithm was tested extensively on both the 16- and 64-slice CT scanners. The efficacy of the algorithm is clearly demonstrated by multiple experiments.

关键词： filtered backprojection algorithm LONG-OBJECT PROBLEM COMPUTED-TOMOGRAPHY IMAGE-RECONSTRUCTION VOLUMETRIC CT SCAN

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Noise-Weighted FBP algorithm for Uniformly Attenuated SPECT Projections

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 2016年第3期63卷 1435-1440页

作者： Zeng, Gengsheng L. Weber State Univ Dept Engn Ogden UT 84408 USA Univ Utah Dept Radiol Salt Lake City UT 84108 USA

Noise-weighted FBP (filtered backprojection) algorithm and Bayesian FBP algorithm were developed recently for un-attenuated Radon transform, which have applications in x-ray CT (computed tomography). This paper extends the noise weighted FBP algorithm to the case of uniformly attenuated Radon transform, and this extended FBP algorithm can be applied in uniformly attenuated SPECT (single photon emission computed tomography). Computer simulations and experimental data demonstrate that the proposed FBP algorithm has similar noise control capability as the iterative ML-EM (maximum likelihood expectation maximization) algorithm. In practice, the attenuator is rarely uniform. A stable FBP algorithm must be developed for non-uniform attenuators before the FBP algorithm can be applied in clinics when attenuation correction is required.

关键词： Attenuated Radon transform exponential Radon transform analytical algorithm Poisson noise filtered backprojection algorithm SPECT

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Revisit of the Ramp Filter

Revisit of the Ramp Filter

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IEEE Nuclear Science Symposium / Medical Imaging Conference (NSS/MIC)

作者： Zeng, Gengsheng L. Weber State Univ Ogden UT 84108 USA Univ Utah Dept Radiol Salt Lake City UT 84108 USA

ISBN: (纸本)9781479960972

关键词： filtered backprojection algorithm analytic image reconstruction

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