ON EXISTENCE AND UNIQUENESS OF THE FORWARD AND INVERSE PROBLEM IN REFRACTIVE INDEX BASED OPTICAL TOMOGRAPHY By
نویسندگان
چکیده
In optical tomography, conventionally the diffusion approximation (DA) to the radiative transport equation (RTE) with a constant refractive index is used. The existence, uniqueness, and non-uniqueness of the forward and the inverse problem using conventional DA has been studied in the past. In this report, we investigate the existence, uniqueness, and non-uniqueness of optical tomography forward and the inverse problem based on the DA to the RTE for a highly scattering medium with a spatially varying refractive index. We establish criteria for existence and uniqueness of solutions. In particular, we derive a nonlinear partial differential equation for the parameter constraint whose unique solvability guarantees uniqueness of the inverse problem.
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