Inverse Problem In Optical Tomography Using Diffusion Approximation and Its Hopf-Cole Transformation
نویسنده
چکیده
In this paper, we derive the Hopf-Cole transformation to the diffusion approximation. We find the analytic solution to the one dimensional diffusion approximation and its Hopf-Cole transformation for a homogenous constant background medium. We demonstrate that for a homogenous constant background medium in one dimension, the Hopf-Cole transformation improves the stability of the inverse problem. We also derive a Green’s function scaling of the higher dimensional diffusion approximation for an inhomogeneous background medium and discuss a two step reconstruction algorithm.
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تاریخ انتشار 2003