Born expansion and Fréchet derivatives in nonlinear Diffuse Optical Tomography

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 mth order Born approximation. Then, we derive the mth order Fréchet derivatives of the coefficient-to-measurement operator using the relationship between the Fréchet derivatives and the Born expansion.