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We revisit the inverse source problem in a two dimensional absorbing andscattering medium and present a non-iterative reconstruction method usingmeasurements of the radiating flux at the boundary. The attenuation andscattering coefficients are known and the unknown source is isotropic. Theapproach is based on the Cauchy problem for a Beltrami-like equation for thesequence valued maps, and extends the original ideas of A. Bukhgeim from thenon-scattering to scattering media. We demonstrate the feasibility of themethod in a numerical experiment in which the scattering is modeled by the twodimensional Henyey-Greenstein kernel with parameters meaningful in OpticalTomography.

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