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Creators/Authors contains: "Sadiq, Kamran"

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  1. ; ; (, SIAM Journal on Imaging Sciences)
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  2. ; (, Inverse Problems and Imaging)
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  3. ; ; (, Inverse Problems)
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  4. ; ; (, 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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  5. ; ; (, SIAM Journal on Imaging Sciences)
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  6. ; ; (, 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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