The Second-Order Born Approximation in Diffuse Optical Tomography

[摘要] Diffuse optical tomography is used to find the optical parametersof 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 photondensity distribution on the boundary of the region of interest, whichis also represented by the Born expansion with respect to the unperturbedphoton densities and perturbed optical coefficients. We suggest a newmethod of finding the solution by using the second-order Born approximation of the operator. The error analysis for the suggested methodbased on the second-order Born approximation is presentedand 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.

[学科分类] 应用数学