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

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

scholarly journals Inversion of the Attenuated X-Ray Transforms: Method of Riesz Potentials

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yu Yufeng
Keyword(s):  
Single Photon ◽  
Photon Emission ◽  
Emission Computed Tomography ◽  
Riesz Potentials ◽  
X Ray ◽  
Ray Transform ◽  
Straight Line ◽  
Single Photon Emission Computed ◽  
Ray Transforms ◽  
Photon Emission Computed Tomography

The attenuated X-ray transform arises from the image reconstruction in single-photon emission computed tomography. The theory of attenuated X-ray transforms is so far incomplete, and many questions remain open. This paper is devoted to the inversion of the attenuated X-ray transforms with nonnegative varying attenuation functions μ, integrable on any straight line of the plane. By constructing the symmetric attenuated X-ray transform Aμ on the plane and using the method of Riesz potentials, we obtain the inversion formula of the attenuated X-ray transforms on Lpℝ21≤p<2 space, with nonnegative attenuation functions μ, integrable on any straight line in ℝ2. These results are succinct and may be used in the type of computerized tomography with attenuation.

Sign in / Sign up

Export Citation Format

Share Document