A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium. (19th December 2019)

• Record Type: Journal Article
• Authors: Fujiwara, Hiroshi; Sadiq, Kamran; Tamasan, Alexandru
• Is Part Of: Inverse problems. Volume 36:Number 1(2020)
• Publication Date: 2019-12-19
• Subjects: attenuated x-ray transform -- attenuated Radon transform -- scattering -- A-analytic maps -- Hilbert transform -- Bukhgeim–Beltrami equation -- optical tomography; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab4d98
• Languages: English
• ISSNs: 0266-5611

Abstract

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.