A robust method of x-ray source spectrum estimation from transmission measurements: Demonstrated on computer simulated, scatter-free transmission data

Sidky, Emil Y.; Yu, Lifeng; Pan, Xiaochuan; Zou, Yu; Vannier, Michael W.

doi:10.1063/1.1928312

Cited by 135 publications

(134 citation statements)

References 16 publications

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“…16 Therefore, the initial guess for the EM method was constructed by multiplying a generic tungsten anode x-ray tube spectrum 3 by the detector response function ͑Gd 2 O 2 S; area mass density 1.05 g / cm 2 ͒, so that the spectrum contained both the characteristics from the x-ray tube and the K-edges from the detector.…”

Section: Iic Experimental Proceduresmentioning

confidence: 99%

“…[7][8][9][10][11][12][13][14][15][16] The transmission method is one of the measurement-based methods. This method is relatively simple and has been implemented in a large range of x-ray energies.…”

Section: Introductionmentioning

confidence: 99%

“…This method is relatively simple and has been implemented in a large range of x-ray energies. [14][15][16][17][18] Transmission methods usually consist of two steps: ͑1͒ Measuring the transmission data for different thicknesses of materials and ͑2͒ reconstructing the spectra by solving the linear equations that represent the attenuation processes of x-ray photons. In this study, an expectation maximization ͑EM͒ method was used to solve the equations.…”

Section: Introductionmentioning

confidence: 99%

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CT scanner x‐ray spectrum estimation from transmission measurements

Duan¹,

Wang²,

Yu³

et al. 2011

Medical Physics

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Purpose:In diagnostic CT imaging, multiple important applications depend on the knowledge of the x-ray spectrum, including Monte Carlo dose calculations and dual-energy material decomposition analysis. Due to the high photon flux involved, it is difficult to directly measure spectra from the x-ray tube of a CT scanner. One potential method for indirect measurement involves estimating the spectrum from transmission measurements. The expectation maximization ͑EM͒ method is an accurate and robust method to solve this problem. In this article, this method was evaluated in a commercial CT scanner. Methods: Two step-wedges ͑polycarbonate and aluminum͒ were used to produce different attenuation levels. Transmission measurements were performed on the scanner and the measured data from the scanner were exported to an external computer to calculate the spectra. The EM method was applied to solve the equations that represent the attenuation processes of polychromatic x-ray photons. Estimated spectra were compared to the spectra simulated using a software provided by the manufacturer of the scanner. To test the accuracy of the spectra, a verification experiment was performed using a phantom containing different depths of water. The measured transmission data were compared to the transmission values calculated using the estimated spectra. Results: Spectra of 80, 100, 120, and 140 kVp from a dual-source CT scanner were estimated. The estimated and simulated spectra were well matched. The differences of mean energies were less than 1 keV. In the verification experiment, the measured and calculated transmission values were in excellent agreement. Conclusions: Spectrum estimation using transmission data and the EM method is a quantitatively accurate and robust technique to estimate the spectrum of a CT system. This method could benefit studies relying on accurate knowledge of the x-ray spectra from CT scanner.

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Section: Iic Experimental Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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CT scanner x‐ray spectrum estimation from transmission measurements

Duan¹,

Wang²,

Yu³

et al. 2011

Medical Physics

Self Cite

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“…The matrix A mn ¼ e −μ n t m contains the properties of the attenuator at the energy corresponding to the n-th energy bin and for the thickness used in the m-th transmission measurement. Once the transmission curve T has been measured, we iteratively apply the set of equations [14,17,22,23] …”

Section: Methodsmentioning

confidence: 99%

“…Information about this distribution is recovered by using a series of attenuation measurements in which the spectrum is progressively modified by varying the filtration. A number of different approaches have been proposed for the solution of this problem, including the use of the Laplace transform, least squares methods, singular value decomposition and iterative approaches [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In this work we focus on the application to experimental data of the expectation-maximization method [14,17] to iteratively solve the ill-conditioned linear system that relates the spectral distribution of the X-ray beam to its transmission.…”

Section: Introductionmentioning

confidence: 99%

Application of an expectation maximization method to the reconstruction of X-ray-tube spectra from transmission data

Endrizzi

Delogu

Oliva

2014

Spectrochimica Acta Part B: Atomic Spectroscopy

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Abstract\ud An expectation maximization method is applied to the reconstruction of X-ray tube spectra from transmission measurements in the energy range 7-40 keV. A semiconductor single-photon counting detector, ionization chambers and a scintillator-based detector are used for the experimental measurement of the transmission. The number of iterations required to reach an approximate solution is estimated on the basis of the measurement error, according to the discrepancy principle. The effectiveness of the stopping rule is studied on simulated data and validated with experiments. The quality of the reconstruction depends on the information available on the source itself and the possibility to add this knowledge to the solution process is investigated. The method can produce good approximations provided that the amount of noise in the data can be estimated. (C) 2014 Elsevier B.V. All rights reserved

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Regularization of nonlinear decomposition of spectral x‐ray projection images

et al. 2017

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Purpose: Exploiting the x-ray measurements obtained in different energy bins, spectral computed tomography (CT) has the ability to recover the 3-D description of a patient in a material basis. This may be achieved solving two subproblems, namely the material decomposition and the tomographic reconstruction problems. In this work, we address the material decomposition of spectral x-ray projection images, which is a nonlinear ill-posed problem. Methods: Our main contribution is to introduce a material-dependent spatial regularization in the projection domain. The decomposition problem is solved iteratively using a Gauss-Newton algorithm that can benefit from fast linear solvers. A Matlab implementation is available online. The proposed regularized weighted least squares Gauss-Newton algorithm (RWLS-GN) is validated on numerical simulations of a thorax phantom made of up to five materials (soft tissue, bone, lung, adipose tissue, and gadolinium), which is scanned with a 120 kV source and imaged by a 4-bin photon counting detector. To evaluate the method performance of our algorithm, different scenarios are created by varying the number of incident photons, the concentration of the marker and the configuration of the phantom. The RWLS-GN method is compared to the reference maximum likelihood Nelder-Mead algorithm (ML-NM). The convergence of the proposed method and its dependence on the regularization parameter are also studied. Results: We show that material decomposition is feasible with the proposed method and that it converges in few iterations. Material decomposition with ML-NM was very sensitive to noise, leading to decomposed images highly affected by noise, and artifacts even for the best case scenario. The proposed method was less sensitive to noise and improved contrast-to-noise ratio of the gadolinium image. Results were superior to those provided by ML-NM in terms of image quality and decomposition was 70 times faster. For the assessed experiments, material decomposition was possible with the proposed method when the number of incident photons was equal or larger than 10 5 and when the marker concentration was equal or larger than 0.03 gÁcm À3 . Conclusions: The proposed method efficiently solves the nonlinear decomposition problem for spectral CT, which opens up new possibilities such as material-specific regularization in the projection domain and a parallelization framework, in which projections are solved in parallel.

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A robust method of x-ray source spectrum estimation from transmission measurements: Demonstrated on computer simulated, scatter-free transmission data

Cited by 135 publications

References 16 publications

CT scanner x‐ray spectrum estimation from transmission measurements

CT scanner x‐ray spectrum estimation from transmission measurements

Application of an expectation maximization method to the reconstruction of X-ray-tube spectra from transmission data

Regularization of nonlinear decomposition of spectral x‐ray projection images

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