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

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, Wμ=R, where W is the weight function, μ 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. © 1998 Society of Photo-Optical Instrumentation Engineers.