A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium

Alexandru Tamasan; Hiroshi Fujiwara; Kamran Sadiq

A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium

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arxiv 1907.07423 v1 pith:BGMVNSA2 submitted 2019-07-17 math.AP math.CV

Hiroshi Fujiwara , Kamran Sadiq , Alexandru Tamasan This is my paper · ORCID

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keywords scatteringproblemsourceabsorbingapproachdimensionalinversemedium

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We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method 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 A. Bukhgeim from the non-scattering to 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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Inverse source problems in transport via attenuated tensor tomography
math.AP 2019-08 conditional novelty 6.0 of 10

For simple 2D geometries, the scattering transport inverse source problem is injective for isotropic and vector sources, and the gauge for higher-degree sources is fully described.

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