Stationary inverse problems for transport
In this talk, we will review prior and recent work on the reconstruction of (1) an isotropic kernel, or (2) a source term, in the radiative transfer equation from measured outgoing radiation.
In the first case, past works joint with Bal, Jollivet and Langmore, assess the stability of reconstructing an isotropic kernel from isotropic sources and angularly averaged albedo measurements, with an increase in stability as one passes from a stationary to time-harmonic setting. The work involves an analogy with Calderon's problem in the stationary setting, and the improvements in the time-harmonic setting are obtained by stationary phase arguments.
In the second problem, we discuss ongoing work with Bal, where an analogy with the attenuated tensor tomography problem allows to uniquely reconstruct a source term, in the case where the scattering kernel is a convolution kernel of finite harmonic
content. This problem arises in Optical Molecular Imaging, and allows to drop smallness assumptions existing in prior work.