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Award ID contains: 1907097

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  1. ; ; (, Inverse Problems)
    Abstract We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a direct reconstruction method, which does not require iterative solvability of the forward problem, using measurements of the radiating flux at the boundary. The attenuation and scattering coefficients are known and the unknown source is isotropic. The approach is based on the Cauchy problem for a Beltrami-like equation for the sequence valued maps, and extends the original ideas of Bukhgeim from the non-scattering to the scattering media. We demonstrate the feasibility of the method in a numerical experiment in which the scattering is modeled by the two dimensional Henyey–Greenstein kernel with parameters meaningful in optical tomography. 
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  2. ; ; (, SIAM Journal on Imaging Sciences)
    Full Text Available 
  3. ; (, Inverse Problems and Imaging)
    Full Text Available 
  4. ; ; (, Inverse Problems)
    Full Text Available 
  5. ; ; (, Suuri kaiseki kenkyuujo koukyuuroku)
    Ohe, Takashi (Ed.)
    We explain how the theory of A-analytic maps can apply to a local CT-inversion problem, in which the data is restricted on an arc. 
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    Accepted Manuscript Full Text Available
  6. ; ; (, Inverse Problems & Imaging)
    null (Ed.)
    In two dimensions, we consider the problem of inversion of the attenuated \begin{document}$ X $$\end{document}-ray transform of a compactly supported function from data restricted to lines leaning on a given arc. We provide a method to reconstruct the function on the convex hull of this arc. The attenuation is assumed known. The method of proof uses the Hilbert transform associated with \begin{document}$$ A $$\end{document}$-analytic functions in the sense of Bukhgeim. 
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    Full Text Available 
  7. ; ; ; (, Keisan suri kogaku ronbunshu)
    The present paper proposes a novel numerical scheme to X-ray Computerized Tomography (CT) from partial measurement data. In order to reduce radiation exposure, it is desirable to irradiate X-ray only around region of interest (ROI), while the conventional reconstruction methods such as filtered back projection (FBP) could not work due to its intrinsic limitation of dependency on whole measurement data. The proposed method gives a direct numerical reconstruction employing a Cauchy type boundary integration in $$A$$-analytic theory and a singular integral equation which maps boundary measurement to interior data. Numerical examples using experimental data are also exhibited to show validity of the proposed numerical procedure. 
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    Accepted Manuscript Full Text Available
  8. ; (, Applied Numerical Mathematics)
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  9. ; ; (, SIAM Journal on Imaging Sciences)
    Full Text Available 
  10. ; (, Keisan suuri kougaku rombunshuu)
    This paper presents a new algorithm for X-ray Computerized Tomography (CT) based on Bukhgeim’s theory of analytic maps. The reconstruction relies on a Cauchy-type integral formula, where the integration over the boundary replaces the integration in the back- projection operator used in existing algorithms. From the numerical computation stand point, the proposed method recovers the attenuation coefficient at arbitrarily points by utilizing the boundary integration without internal global meshes. This means that it achieves high-parallel efficiency, and it reduces computational resources. Some numerical examples are presented to show feasibility of the proposed algorithm. 
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    Accepted Manuscript Full Text Available