An inverse source problem in radiative transfer with partial data

Abstract

The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a certain subset of the domain, which we call the visible set. Furthermore, it is shown for an open dense set of C∞ absorption and scattering coefficients that one can recover the part of the wavefront set of the source that is supported in the microlocally visible set, modulo a function in the Sobolev space Hk for k arbitrarily large. This is an extension to the full data case, where the complete recovery of an arbitrary source has been shown.