Dependence of optical diffusion tomography image quality on image operator and noise

By applying linear perturbation theory to the radiation transport equation, the inverse problem of optical diffusion tomography can be reduced to a set of linear equations, W_μ=R, where W is the weight function, μ is the cross section perturbations to be imaged, and R is the detector readings perturbations. The quality of reconstructed images depends on the accuracy of W and R, and was studied by corrupting one or both with systematic error and/or random noise. Monte Carlo simulations (MCS) performed on a cylindrical phantom of 20 mean free paths (mfp) diameter, with and without a black absorber located off-axis, were used to compute R and W (i.e., matched W). Additional MCS computed Ws for cylinders of 10 mfp, 40 mfp, and 100 mfp diameters (i.e., unmatched W). R and/or W also were corrupted with additive white noise. A constrained CGD method the authors developed was used to reconstruct images from the simulated R and Ws. The results show that images containing few artifacts and the rod accurately located can be obtained when the matched W is used. Comparable image quality was obtained for unmatched Ws, but the location of the rod becomes more inaccurate as the mismatch increases. The noise study shows that W is much more sensitive than R to noise. The rod can be reasonably located with 100% noise added to R, while addition of 5% noise to W totally destroys the image. The impact of noise increases with the number of iterations