Near-Infrared Medical Imaging: Improved Approximations for the Forward and Inverse Problems

We consider imaging of objects hidden in a scattering and absorbing medium, thick enough for the diffusion approximation to be valid, e.g. mammography or brain activity studies. We propose approximate models improving over Born to calculate the image: the electrostatic approximation if the object is small, plus a renormalization transform if it is larger. Using an exact solution of the ‘sphere in slab’ problem for comparison, and a Bayesian simplified inverse code, we demonstrate that these approximations improve the reconstruction.