# Dependence of Optical Diffusion Tomography Image Quality on Image Operator and Noise

### J. Chang *et al.* (1995)

#### Summary

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 **W**s for cylinders of 10
mfp, 40 mfp, and 100 mfp diameters (*i.e.*, *un*matched **W**). **R** and/or **W** also were
corrupted with additive white noise. A constrained CGD method we developed was used to reconstruct images from the simulated
**R** and **W**s. 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 the unmatched **W**s, 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% to **W** totally destroys the image. The impact of noise increases with the number of iterations.