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Born expansion and Fréchet derivatives in nonlinear diffuse optical tomography. (English) Zbl 1197.35282
Summary: The nonlinear Diffuse Optical Tomography (DOT) problem involves the inversion of the associated coefficient-to-measurement operator, which maps the spatially varying optical coefficients of turbid medium to the boundary measurements. The inversion of the coefficient-to-measurement operator is approximated by using the Fréchet derivative of the operator. In this work, we first analyze the Born expansion, show the conditions which ensure the existence and convergence of the Born expansion, and compute the error in the \(m\)th order Born approximation. Then, we derive the \(m\)th order Fréchet derivatives of the coefficient-to-measurement operator using the relationship between the Fréchet derivatives and the Born expansion.

MSC:
35Q60 PDEs in connection with optics and electromagnetic theory
78A55 Technical applications of optics and electromagnetic theory
92C55 Biomedical imaging and signal processing
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