منابع مشابه
The Attenuated X-ray Transform: Recent Developments
We survey recent work on the attenuated x-ray transform, concentrating especially on the inversion formulas found in the last few years.
متن کاملThe Geodesic X-ray Transform with Fold Caustics
We give a detailed microlocal study of X-ray transforms over geodesics-like families of curves with conjugate points of fold type. We show that the normal operator is the sum of a pseudodifferential operator and a Fourier integral operator. We compute the principal symbol of both operators and the canonical relation associated to the Fourier integral operator. In two dimensions, for the geodesi...
متن کاملInverting the Local Geodesic X-ray Transform on Tensors
We prove the local invertibility, up to potential fields, and stability of the geodesic X-ray transform on tensor fields of order 1 and 2 near a strictly convex boundary point, on manifolds with boundary of dimension n ≥ 3. We also present an inversion formula. Under the condition that the manifold can be foliated with a continuous family of strictly convex surfaces, we prove a global result wh...
متن کاملThe Identification Problem for the Attenuated X-ray Transform
We study the problem of recovery both the attenuation a and the source f in the attenuated X-ray transform in the plane. We study the linearization as well. It turns out that there is a natural Hamiltonian flow that determines which singularities we can recover. If the perturbation δa is supported in a compact set that is non-trapping for that flow, then the problem is well posed. Otherwise, it...
متن کاملThe X-ray Transform and its Application in Nano Crystallography
In this article a review on the definition of the X- ray transform and some ofits applications in Nano crystallography is presented. We shall show that the X- raytransform is a special case of the Radon transform on homogeneous spaces when thetopological group E(n)- the Euclidean group - acts on ℝ2 transitively. First someproperties of the Radon transform are investigated then the relationship ...
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ژورنال
عنوان ژورنال: Inverse Problems
سال: 2018
ISSN: 0266-5611,1361-6420
DOI: 10.1088/1361-6420/aab8bc