On the inverse problem and Sobolev estimates of the generalized X-ray transform

2021 ◽  
pp. 1-15
Author(s):  
Wei Li ◽  
Jinping Wang
Keyword(s):  
Inverse Problem ◽  
X Ray ◽  
Ray Transform ◽  
Sobolev Estimates

scholarly journals X-ray Transform in Asymptotically Conic Spaces

2020 ◽  
Author(s):  
Colin Guillarmou ◽  
Matti Lassas ◽  
Leo Tzou
Keyword(s):  
Inverse Problem ◽  
Conjugate Point ◽  
Riemannian Metrics ◽  
X Ray ◽  
Ray Transform

Abstract In this article, we study the properties of the geodesic X-ray transform for asymptotically Euclidean or conic Riemannian metrics and show injectivity under non-trapping and no conjugate point assumptions. We also define a notion of lens data for such metrics and study the associated inverse problem.

scholarly journals Invertibility of multi‐energy x‐ray transform

2021 ◽  
Author(s):  
Yijun Ding ◽  
Eric W. Clarkson ◽  
Amit Ashok
Keyword(s):  
X Ray ◽  
Ray Transform

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 On the injectivity of the X-ray transform for Anosov thermostats

2009 ◽  
Vol 24 (2) ◽  
pp. 471-487 ◽  
Author(s):  
Dan Jane ◽  
◽  
Gabriel P. Paternain
Keyword(s):  
X Ray ◽  
Ray Transform

scholarly journals $L^{p}$ estimates for the $X$-ray transform

1983 ◽  
Vol 27 (1) ◽  
pp. 125-129 ◽  
Author(s):  
S. W. Drury
Keyword(s):  
X Ray ◽  
Ray Transform

The Spherical X-Ray Transform of Texture Goniometry

2001 ◽  
pp. 283-291 ◽  
Author(s):  
Helmut Schaeben ◽  
Wolfgang Sprößig ◽  
Gerald Boogaart
Keyword(s):  
X Ray ◽  
Ray Transform
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