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

In frequency-domain optical diffusion imaging, the magnitude and the phase of modulated light propagated through a highly scattering medium are used t o 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 th e reconstructions and the speed of convergence. In particular, conventional integral equation approaches such as the Born iterative method and the dis torted Born iterative method can suffer from slow convergence, especially f or large spatial variations in the constitutive parameters. We show that sl ow convergence of conventional algorithms is due to the linearized integral equations' not being the correct Frechet derivative with respect to the ab sorption and scattering coefficients. The correct Frechet derivative operat or is derived here. However, the Frechet 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 imag ing data. To ameliorate these effects we derive an approximation to the Fre chet derivative and implement it in an inversion algorithm. Simulation resu lts show that this inversion algorithm outperforms conventional iterative m ethods. (C) 1999 Optical Society of America [S0740-3532(99)02907-5].