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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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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

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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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Noise weighting with an exponent for transmission CT

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BIOMEDICAL PHYSICS & ENGINEERING EXPRESS 2016年第4期2卷 045004页

作者： Zeng, Gengsheng L. Wang, Wenli Weber State Univ Dept Engn Ogden UT 84408 USA Univ Utah Dept Radiol Salt Lake City UT 84108 USA Toshiba Med Res Inst USA Inc Vernon Hills IL 60061 USA

It is widely believed that the correct weighting function is the reciprocal of the noise variance of the associated measurement. Many researchers are making great efforts to find the accurate variance for the measurements for imaging systems so that they can hopefully achieve an optimal reconstruction. An 'optimal' solution in the context of this paper is referred to as the image that reaches optimum according to a criterion or criteria among a group of candidates, regardless how the images in the group are obtained. This 'optimal' solution is not a theoretical concept, but is simply the ` best of the bunch'. The goal of the paper is to investigate how the weighting function affects the image noise when the image contrast is pre-specified in an iterative algorithm for x-ray CT. This paper makes some interesting observations: there is no universal optimal weighting function. The noise weighting function can introduce artifacts. The optimal noise weighting varies with the object to be reconstructed and targeted image contrast in an iterative image reconstruction algorithm and in a filtered backprojection algorithm that incorporates the projection noise. It is suggested that an exponent be used in the weighting function so that the artifacts caused by the weighting function can be reduced.

关键词： computed tomography iterative reconstruction filtered backprojection algorithm noise weighted image reconstruction

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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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High Frequency Ultrasound Computed Tomography for Small Animal Imaging Applications

High Frequency Ultrasound Computed Tomography for Small Anim...

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IEEE International Ultrasonics Symposium (IUS)

作者： Chen, Wei-Tsen Shih, Cho-Chiang Huang, Chih-Chung Fu Jen Catholic Univ Dept Elect Engn New Taipei City Taiwan

ISBN: (纸本)9781457712524

This study developed a high frequency ultrasound computed tomography (UCT) imaging system for small animal imaging. Both attenuation and sound velocity UCT were used to recognize the tissue properties with a high image contrast. The center frequencies of transducers ranging from 25 to 40 MHz were used in this system. The high frequency transducer was mounted on a three axes step motor system for linear scan, and the object was fixed on a rotational stage which was controlled by another step motor. The projections of object at different angles were obtained by measuring the sound speed and relative attenuation passed through the object. The filtered backprojection algorithm was used to reconstruct the two dimensional UCT image. The resolution of the system was verified by scanning a 200 mu m diameter micro-tube. The system verification was performed by imaging the gelatin phantoms and zebrafish. In phantom experiments, the phantom was composed of two different gelatins (gelatin concentration for 4% and 6%). In contrast to ultrasound B-mode image, the slight difference in different concentration gelatins can be recognized easily by using the UCT system. For small animal experiments, most organs of zebrafish can be observed by high frequency UCT images. All the results indicate that the UCT has great potential applications in imaging small animal, such as zebrafish liver tumor and rat testicle.

关键词： High-frequency ultrasound Ultrasound computed tomography filtered backprojection algorithm Zebrafish

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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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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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Diffuse optical tomogram restoration with spatially variant point spread function - art. no. 62570Q

Diffuse optical tomogram restoration with spatially variant ...

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ICONO 2005 Conference

作者： Konovalov, AB Russian Fed Nucl Ctr Inst Tech Phys Snezhinsk 456770 Chelyabinsk Reg Russia

ISBN: (纸本)0819463167

The possibility of improving the spatial resolution of diffuse optical tomograms reconstructed by the photon average trajectories (PAT) method is substantiated. The PAT method is based on a concept of an average statistical trajectory for transfer of light energy, the photon average trajectory (PAT). The inverse problem of diffuse optical tomography is reduced to a solution of an integral equation with integration along a conditional PAT. As a result, the standard filtered backprojection algorithm can be used for fast reconstruction of diffuse optical tomograms. The shortcoming of the PAT method is that it reconstructs the images blurred due to averaging over spatial distributions of photons, which form the signal measured by the receiver. To improve the resolution, I apply a spatially variant blur model based on an interpolation of the spatially invariant point spread functions simulated for the different small sub-regions of the image domain. Two iterative algorithms for solving a system of linear algebraic equations: the conjugate gradient algorithm for least squares problem and the modified residual norm steepest descent algorithm are used for deblurring. It is shown that the restoration procedure enhances the tomogram profiles and allows an obvious gain in spatial resolution to be obtained.

关键词： diffuse optical tomography filtered backprojection algorithm spatially variant blur model image restoration

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