Modified distorted Born iterative method with an approximate Fréchet derivative for optical diffusion tomography

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Abstract
In frequency-domain optical diffusion imaging, the magnitude and the phase of modulated light propagated through a highly scattering medium are used to reconstruct an image of the scattering and absorption coefficients in the medium. Although current reconstruction algorithms have been applied with some success, there are opportunities for improving both the accuracy of the reconstructions and the speed of convergence. In particular, conventional integral equation approaches such as the Born iterative method and the distorted Born iterative method can suffer from slow convergence, especially for large spatial variations in the constitutive parameters. We show that slow convergence of conventional algorithms is due to the linearized integral equations’ not being the correct Fréchet derivative with respect to the absorption and scattering coefficients. The correct Fréchet derivative operator is derived here. However, the Fréchet derivative suffers from numerical instability because it involves gradients of both the Green’s function and the optical flux near singularities, a result of the use of near-field imaging data. To ameliorate these effects we derive an approximation to the Fréchet derivative and implement it in an inversion algorithm. Simulation results show that this inversion algorithm outperforms conventional iterative methods.