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Journal of Applied Mathematics
Volume 2012, Article ID 637209, 15 pages
http://dx.doi.org/10.1155/2012/637209
Research Article

The Second-Order Born Approximation in Diffuse Optical Tomography

Department of Mathematics, Dongguk University, Seoul 100715, Republic of Korea

Received 21 October 2011; Accepted 8 December 2011

Academic Editor: Chang-Hwan Im

Copyright © 2012 Kiwoon Kwon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Diffuse optical tomography is used to find the optical parameters of a turbid medium with infrared red light. The problem is mathematically formulated as a nonlinear problem to find the solution for the diffusion operator mapping the optical coefficients to the photon density distribution on the boundary of the region of interest, which is also represented by the Born expansion with respect to the unperturbed photon densities and perturbed optical coefficients. We suggest a new method of finding the solution by using the second-order Born approximation of the operator. The error analysis for the suggested method based on the second-order Born approximation is presented and compared with the conventional linearized method based on the first-order Born approximation. The suggested method has better convergence order than the linearized method, and this is verified in the numerical implementation.