scholarly journals Consistent Inversion of Noisy Non‐Abelian X‐Ray Transforms

2020 ◽  
Author(s):  
François Monard ◽  
Richard Nickl ◽  
Gabriel P. Paternain
Keyword(s):  
X Ray ◽  
Ray Transforms

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.

estimates for restricted X-ray transforms, II

1991 ◽  
Vol 64 (3) ◽  
pp. 415-444 ◽  
Author(s):  
Allan Greenleaf ◽  
Gunther Uhlmann
Keyword(s):  
X Ray ◽  
Ray Transforms

scholarly journals Uniform bounds for convolution and restricted X-ray transforms along degenerate curves

2015 ◽  
Vol 268 (3) ◽  
pp. 585-633 ◽  
Author(s):  
Spyridon Dendrinos ◽  
Betsy Stovall
Keyword(s):  
Uniform Bounds ◽  
X Ray ◽  
Ray Transforms

scholarly journals Reconstruction formulas for X-ray transforms in negative curvature

2017 ◽  
Vol 67 (4) ◽  
pp. 1353-1392 ◽  
Author(s):  
Colin Guillarmou ◽  
François Monard
Keyword(s):  
Negative Curvature ◽  
X Ray ◽  
Ray Transforms

scholarly journals Efficient nonparametric Bayesian inference for $X$-ray transforms

2019 ◽  
Vol 47 (2) ◽  
pp. 1113-1147 ◽  
Author(s):  
François Monard ◽  
Richard Nickl ◽  
Gabriel P. Paternain
Keyword(s):  
Bayesian Inference ◽  
Nonparametric Bayesian ◽  
X Ray ◽  
Ray Transforms
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