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Numerical reconstruction of radiative sources in an absorbing and nondiffusing scattering medium in two dimensions. (English) Zbl 1447.65118

The numerical reconstruction of radiative sources in an absorbing and nondiffusing scattering medium is considered. The unknown source is determined from the measurement of the directional outflow at the boundary of a bounded, strictly convex domain in two dimensions. The basis of the presented numerical reconstruction method are theoretical results obtained by the authors of that paper (see [H. Fujiwara et al., Inverse Probl. 36, No. 1, Article ID 015005, 33 p. (2020; Zbl 1433.78016)]). The authors describe the basic ideas of the reconstruction algorithm and the main ingredients of the numerical implementation, e.g., the evaluation of the Hilbert transform and the computation of the Cauchy-type integral formula. Then, the reconstruction algorithm is presented. The algorithm is demonstrated by two numerical examples.

MSC:

65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
44A15 Special integral transforms (Legendre, Hilbert, etc.)
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
35Q60 PDEs in connection with optics and electromagnetic theory
44A12 Radon transform

Citations:

Zbl 1433.78016

Software:

PET; FreeFem++
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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