The broken ray transform: additional properties and new inversion formula
نویسندگان
چکیده
منابع مشابه
Inversion formulas for the broken-ray Radon transform
The inverse transport problem consists of recovering the spatially varying absorption and scattering coefficients of the interior of a highly scattering medium from measurements taken on its boundary [2]. The problem has been widely studied in the context of optical tomography (OT)—a biomedical imaging modality that makes use of multiply-scattered light to visualize structural variations in the...
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The Fourier transform is the basic and most powerful tool for studying translation invariant analytic problems, such as constant coefficient PDE on R. It is based on the following simple observation: for ξ ∈ R, the functions vξ(x) = e ix·ξ = e11 · · · enn are joint eigenfunctions of the operators ∂xj , namely for each j, (1) ∂xjvξ = iξjvξ. It would thus be desirable to decompose an ‘arbitrary’ ...
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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: 2019
ISSN: 0266-5611,1361-6420
DOI: 10.1088/1361-6420/ab355f