scholarly journals An extrapolation method for projection data fltration in pulsed X-ray tomography

2021 ◽  
Vol 2099 (1) ◽  
pp. 012050
Author(s):  
I P Yarovenko ◽  
I V Prokhorov
Keyword(s):  
Inverse Problem ◽  
Numerical Experiments ◽  
Radiation Transfer ◽  
Projection Data ◽  
Radiation Transfer Equation ◽  
Scattering Medium ◽  
X Ray ◽  
Coefficient Identification ◽  
Reconstruction Quality ◽  
Stationary Radiation

Abstract This paper deals with an inverse problem that consists of an attenuation coefficient identification for the non-stationary radiation transfer equation. To solve the problem, we propose a method that uses several pulses of radiation to extrapolate ideal projection data corresponding to a non-scattering medium. Numerical experiments on the Shepp-Logan phantom show that the method proposed improves the reconstruction quality.

A Spectrum-Adaptive Decomposition Method for Effective Atomic Number Estimation Using Dual Energy CT

2020 ◽  
Vol 2020 (14) ◽  
pp. 293-1-293-7
Author(s):  
Ankit Manerikar ◽  
Fangda Li ◽  
Avinash C. Kak
Keyword(s):  
Atomic Number ◽  
Decomposition Method ◽  
Traditional Approach ◽  
Effective Atomic Number ◽  
Dual Energy ◽  
Performance Comparison ◽  
Estimation Methods ◽  
Dual Energy Ct ◽  
Projection Data ◽  
X Ray

Dual Energy Computed Tomography (DECT) is expected to become a significant tool for voxel-based detection of hazardous materials in airport baggage screening. The traditional approach to DECT imaging involves collecting the projection data using two different X-ray spectra and then decomposing the data thus collected into line integrals of two independent characterizations of the material properties. Typically, one of these characterizations involves the effective atomic number (Zeff) of the materials. However, with the X-ray spectral energies typically used for DECT imaging, the current best-practice approaches for dualenergy decomposition yield Zeff values whose accuracy range is limited to only a subset of the periodic-table elements, more specifically to (Z < 30). Although this estimation can be improved by using a system-independent ρe — Ze (SIRZ) space, the SIRZ transformation does not efficiently model the polychromatic nature of the X-ray spectra typically used in physical CT scanners. In this paper, we present a new decomposition method, AdaSIRZ, that corrects this shortcoming by adapting the SIRZ decomposition to the entire spectrum of an X-ray source. The method reformulates the X-ray attenuation equations as direct functions of (ρe, Ze) and solves for the coefficients using bounded nonlinear least-squares optimization. Performance comparison of AdaSIRZ with other Zeff estimation methods on different sets of real DECT images shows that AdaSIRZ provides a higher output accuracy for Zeff image reconstructions for a wider range of object materials.

scholarly journals Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu ◽  
Wen Ji ◽  
Seungmin Rho
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Sensor Array ◽  
Variational Iteration Method ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Variational Iteration

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.

An inversion formula for the transport equation in ℝ3 using complex analysis in several variables

2019 ◽  
Vol 27 (3) ◽  
pp. 341-352
Author(s):  
Seyed Majid Saberi Fathi
Keyword(s):  
Inverse Problem ◽  
Transport Equation ◽  
Inversion Formula ◽  
Complex Analysis ◽  
Three Dimensional ◽  
Analytical Continuation ◽  
Radon Transforms ◽  
Photon Transport ◽  
X Ray ◽  
Several Variables

Abstract In this paper, the stationary photon transport equation has been extended by analytical continuation from {\mathbb{R}^{3}} to {\mathbb{C}^{3}} . A solution to the inverse problem posed by this equation is obtained on a hyper-sphere and a hyper-cylinder as X-ray and Radon transforms, respectively. We show that these results can be transformed into each other, and they agree with known results. Numerical reconstructions of a three-dimensional Shepp–Logan head phantom using the obtained inverse formula illustrate the analytical results obtained in this manuscript.

scholarly journals Численное моделирование миграции фотонов в однородных и неоднородных цилиндрических фантомах

2020 ◽  
Vol 128 (6) ◽  
pp. 832
Author(s):  
А.Ю. Потлов ◽  
С.В. Фролов ◽  
С.Г. Проскурин
Keyword(s):  
Radiation Transfer ◽  
Biological Tissues ◽  
Photon Density ◽  
Radiation Transfer Equation ◽  
Scattering Media ◽  
Soft Biological Tissues ◽  
Photon Diffusion ◽  
Low Coherence ◽  
The Brain ◽  
Pulsed Irradiation

The specific features of photon diffusion of low-coherence pulsed irradiation in phantoms of soft biological tissues (blood-saturated tissues of the brain, breast, etc.) are described. The results of photon migration simulation using the Diffusion Approximation to the Radiation Transfer Equation (RTE) are compared with ones of the Monte Carlo simulations. It has been confirmed that the Photon Density Normalized Maximum (PDNM) moves towards the center of the investigated object in case of relatively uniform and strongly scattering media. In the presence of inhomogeneities, type of the PDNM motion changes drastically. Presence of an absorbing inhomogeneity in the medium directs trajectory of the PDNM motion of towards the point symmetric to the inhomogeneity relative to the geometric center of the investigated object. In case of scattering the PDNM moves toward the direction of the center of the scattering inhomogeneity.

scholarly journals Three-dimensional propagation in near-field tomographic X-ray phase retrieval

2016 ◽  
Vol 72 (2) ◽  
pp. 215-221 ◽  
Author(s):  
Aike Ruhlandt ◽  
Tim Salditt
Keyword(s):  
Phase Retrieval ◽  
Near Field ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Current Phase ◽  
Computationally Efficient ◽  
X Ray ◽  
Reconstruction Quality ◽  
Consistency Constraints

This paper presents an extension of phase retrieval algorithms for near-field X-ray (propagation) imaging to three dimensions, enhancing the quality of the reconstruction by exploiting previously unused three-dimensional consistency constraints. The approach is based on a novel three-dimensional propagator and is derived for the case of optically weak objects. It can be easily implemented in current phase retrieval architectures, is computationally efficient and reduces the need for restrictive prior assumptions, resulting in superior reconstruction quality.

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