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

### J. Chang *et al.* (1998)

#### 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***m* = **R**, where **W** is the weight function, *m* are the cross-section
perturbations to be imaged, and **R** is the detector readings perturbations. We have studied
the dependence of image quality on added systematic error and/or random noise in **W** and
**R**. Tomographic data were collected from cylindrical phantoms, with and without added
inclusions, using Monte Carlo methods. Image reconstruction was accomplished using a constrained
conjugate gradient descent method. Results show that accurate images containing few artifacts are
obtained when **W** is derived from a reference state whose optical thickness matches that of
the unknown test medium. Comparable image quality was also obtained for unmatched **W**, but
the location of the target becomes more inaccurate as the mismatch increases. Results of the
noise study show that image quality is much more sensitive to noise in **W** than in **R**,
and the impact of noise increases with the number of iterations. Images reconstructed after pure
noise was substituted for **R** consistently contain large peaks clustered about the cylinder
axis, which was an initially unexpected structure. In other words, random input produces a
nonrandom output. This finding suggests that algorithms sensitive to the evolution of this
feature could be developed to suppress noise effects.