scholarly journals Generic uniqueness and stability for the mixed ray transform

2021 ◽  
pp. 1
Author(s):  
Maarten V. de Hoop ◽  
Teemu Saksala ◽  
Gunther Uhlmann ◽  
Jian Zhai
Keyword(s):  
Ray Transform ◽  
Generic Uniqueness

scholarly journals Stability of the Non-abelian X-ray Transform in Dimension $$\ge 3$$

2021 ◽  
Author(s):  
Jan Bohr
Keyword(s):  
Stability Estimate ◽  
Scattering Data ◽  
Regularity Conditions ◽  
Uniform Bounds ◽  
Ray Transform ◽  
Shallow Layer ◽  
Matrix Potential ◽  
Novel Method ◽  
Statistical Consistency ◽  
Appl Math

AbstractNon-abelian X-ray tomography seeks to recover a matrix potential $$\Phi :M\rightarrow {\mathbb {C}}^{m\times m}$$ Φ : M → C m × m in a domain M from measurements of its so-called scattering data $$C_\Phi $$ C Φ at $$\partial M$$ ∂ M . For $$\dim M\ge 3$$ dim M ≥ 3 (and under appropriate convexity and regularity conditions), injectivity of the forward map $$\Phi \mapsto C_\Phi $$ Φ ↦ C Φ was established in (Paternain et al. in Am J Math 141(6):1707–1750, 2019). The present article extends this result by proving a Hölder-type stability estimate. As an application, a statistical consistency result for $$\dim M =2$$ dim M = 2 (Monard et al. in Commun Pure Appl Math, 2019) is generalised to higher dimensions. The injectivity proof in (Paternain et al. in Am J Math 141(6):1707–1750, 2019) relies on a novel method by Uhlmann and Vasy (Invent Math 205(1):83–120, 2016), which first establishes injectivity in a shallow layer below $$\partial M$$ ∂ M and then globalises this by a layer stripping argument. The main technical contribution of this paper is a more quantitative version of these arguments, in particular, proving uniform bounds on layer depth and stability constants.

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
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