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2012 The Second-Order Born Approximation in Diffuse Optical Tomography
Kiwoon Kwon
J. Appl. Math. 2012(SI04): 1-15 (2012). DOI: 10.1155/2012/637209

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.

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Kiwoon Kwon. "The Second-Order Born Approximation in Diffuse Optical Tomography." J. Appl. Math. 2012 (SI04) 1 - 15, 2012. https://doi.org/10.1155/2012/637209

Information

Published: 2012
First available in Project Euclid: 17 October 2012

zbMATH: 1235.78040
MathSciNet: MR2889126
Digital Object Identifier: 10.1155/2012/637209

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI04 • 2012
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