Inverse Problem In Optical Tomography Using Diffusion Approximation and Its Hopf-Cole Transformation

• Main Author: Taufiquar R. Khan
• Format: Article
• Language: English
• Published: International Institute of Informatics and Cybernetics 2003-12-01
• Series: Journal of Systemics, Cybernetics and Informatics
• Subjects: inverse problems; optical tomography; Green's function scaling; Radiative transport; Hopf-Cole transformation
• Online Access: http://www.iiisci.org/Journal/CV$/sci/pdfs/P203028.pdf

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.