scholarly journals EM Estimation of the X-Ray Spectrum With a Genetically Optimized Step-Wedge Phantom

2021 ◽  
Vol 9 ◽  
Author(s):  
Mengzhou Li ◽  
Feng-Lei Fan ◽  
Wenxiang Cong ◽  
Ge Wang
Keyword(s):  
Energy Spectrum ◽  
Condition Number ◽  
Linear Equations ◽  
Spectrum Estimation ◽  
Genetic Optimization ◽  
System Matrix ◽  
X Ray ◽  
Phantom Design ◽  
Selection Of ◽  
Spectrum Inversion

The energy spectrum of an X-ray tube plays an important role in computed tomography (CT), and is often estimated from physical measurement of dedicated phantoms. Usually, this estimation problem is reduced to solving a system of linear equations, which is generally ill-conditioned. In this paper, we optimize a phantom design to find the most effective combinations of thicknesses for different materials. First, we analyze the ill-posedness of the energy spectrum inversion when the number of unknown variables (N) and measurements (M) are equal, and show the condition number of the system matrix increases exponentially with N if the transmission thicknesses are linearly changed. Then, we present a genetic optimization algorithm to minimize the condition number of the system matrix in a general case (M < N) with respect to the selection of thicknesses and types of phantom materials. Finally, in the simulation with Poisson noise we study the accuracy of the spectrum estimation using the expectation-maximum algorithm. Our results indicate that the proposed method allows high-quality spectrum estimation, and the number of measurements is reduced over two thirds of that required by the widely-used method using a phantom with linearly-changed thicknesses.

scholarly journals Segmentation-free x-ray energy spectrum estimation for computed tomography using dual-energy material decomposition

2017 ◽  
Vol 4 (2) ◽  
pp. 023506 ◽  
Author(s):  
Wei Zhao ◽  
Lei Xing ◽  
Qiude Zhang ◽  
Qingguo Xie ◽  
Tianye Niu
Keyword(s):  
Computed Tomography ◽  
Energy Spectrum ◽  
Dual Energy ◽  
Spectrum Estimation ◽  
Material Decomposition ◽  
X Ray ◽  
Energy Material

Semi‐empirical, parametrized spectrum estimation for X‐ray computed tomography

2021 ◽  
Author(s):  
Paul FitzGerald ◽  
Stephen Araujo ◽  
Mingye Wu ◽  
Bruno De Man
Keyword(s):  
Computed Tomography ◽  
Spectrum Estimation ◽  
X Ray ◽  
X Ray Computed ◽  
Semi Empirical

scholarly journals A Multiple and Multi-Level Substructure Method for the Dynamics of Complex Structures

2021 ◽  
Vol 11 (12) ◽  
pp. 5570
Author(s):  
Binbin Wang ◽  
Jingze Liu ◽  
Zhifu Cao ◽  
Dahai Zhang ◽  
Dong Jiang
Keyword(s):  
Structural Characteristics ◽  
Complex Structure ◽  
Complex Structures ◽  
System Matrix ◽  
Substructure Method ◽  
Residual Structure ◽  
The Matrix ◽  
Multi Level ◽  
Fixed Interface ◽  
Selection Of

Based on the fixed interface component mode synthesis, a multiple and multi-level substructure method for the modeling of complex structures is proposed in this paper. Firstly, the residual structure is selected according to the structural characteristics of the assembled complex structure. Secondly, according to the assembly relationship, the parts assembled with the residual structure are divided into a group of substructures, which are named the first-level substructure, the parts assembled with the first-level substructure are divided into a second-level substructure, and consequently the multi-level substructure model is established. Next, the substructures are dynamically condensed and assembled on the boundary of the residual structure. Finally, the substructure system matrix, which is replicated from the matrix of repeated physical geometry, is obtained by preserving the main modes and the constrained modes and the system matrix of the last level of the substructure is assembled to the upper level of the substructure, one level up, until it is assembled in the residual structure. In this paper, an assembly structure with three panels and a gear box is adopted to verify the method by simulation and a rotor is used to experimentally verify the method. The results show that the proposed multiple and multi-level substructure modeling method is not unique to the selection of residual structures, and different classification methods do not affect the calculation accuracy. The selection of 50% external nodes can further improve the analysis efficiency while ensuring the calculation accuracy.

scholarly journals Spectral Tomography for 3D Element Detection and Mineral Analysis

Minerals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 598
Author(s):  
Jose R. A. Godinho ◽  
Gabriel Westaway-Heaven ◽  
Marijn A. Boone ◽  
Axel D. Renno
Keyword(s):  
Energy Spectrum ◽  
3D Imaging ◽  
X Rays ◽  
3D Images ◽  
Characterization Methods ◽  
X Ray ◽  
Additional Information ◽  
Mineral Phases ◽  
Spectral Computed Tomography

This paper demonstrates the potential of a new 3D imaging technique, Spectral Computed Tomography (sp-CT), to identify heavy elements inside materials, which can be used to classify mineral phases. The method combines the total X-ray transmission measured by a normal polychromatic X-ray detector, and the transmitted X-ray energy spectrum measured by a detector that discriminates between X-rays with energies of about 1.1 keV resolution. An analysis of the energy spectrum allows to identify sudden changes of transmission at K-edge energies that are specific of each element. The additional information about the elements in a phase improves the classification of mineral phases from grey-scale 3D images that would be otherwise difficult due to artefacts or the lack of contrast between phases. The ability to identify the elements inside the minerals that compose ore particles and rocks is crucial to broaden the application of 3D imaging in Earth sciences research and mineral process engineering, which will represent an important complement to traditional 2D imaging mineral characterization methods. In this paper, the first applications of sp-CT to classify mineral phases are showcased and the limitations and further developments are discussed.

A Non-Normality Measure of the Condition Number for Monitoring and Control

1997 ◽  
Vol 119 (2) ◽  
pp. 217-222 ◽  
Author(s):  
Kunsoo Huh ◽  
Jeffrey L. Stein
Keyword(s):  
Optimal Control ◽  
Condition Number ◽  
Minimization Problem ◽  
Monitoring And Control ◽  
Proper Selection ◽  
Modal Structure ◽  
L2 Norm ◽  
And Control ◽  
Normality Measure ◽  
Selection Of

Because the behavior of the condition number can have highly steep and multi-modal structure, optimal control and monitoring problems based on the condition number cannot be easily solved. In this paper, a minimization problem is formulated for κ2(P), the condition number of an eigensystem (P) of a matrix in terms of the L2 norm. A new non-normality measure is shown to exist that guarantees small values for the condition number. In addition, this measure can be minimized by proper selection of controller and observer gains. Application to the design of well-conditioned controller and observer-based monitors is illustrated.

Improved spatial resolution and lower-dose pediatric CT imaging: a feasibility study to evaluate narrowing the X-ray photon energy spectrum

2014 ◽  
Vol 44 (8) ◽  
pp. 1026-1030
Author(s):  
Mark G. Benz ◽  
Matthew W. Benz ◽  
Steven B. Birnbaum ◽  
Eric Chason ◽  
Brian W. Sheldon ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Feasibility Study ◽  
Spatial Resolution ◽  
Photon Energy ◽  
Ct Imaging ◽  
X Ray ◽  
Pediatric Ct ◽  
Photon Energy Spectrum
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