Image Reconstruction of Dense Scattering Media from CW Sources Using Constrained CGD and a Matrix Rescaling Technique

J. Chang et al. (1995)

Summary

This study reports on results of our efforts to improve the efficiency and stability of previously developed reconstruction algorithms for optical diffusion tomography. The previous studies, which applied regularization and a priori constraints to iterative methods—POCS, CGD, and SART algorithms—showed that in most cases, good quality reconstructions of simply structured media were achievable using a perturbation model. The CGD method, which is the most efficient of the three algorithms, was, however, in some instances not able to produce good quality images because of the difficulty in applying range constraints, which can cause divergence. In this study, a scheme is proposed to detect this divergence while imposing range constraints on the previous reconstruction. Once divergence is detected, the conjugate gradient vector is rest and the CGD reconstruction is restarted using the previous reconstruction as the initial value. In addition, a rescaling technique, which rescales the weight matrix to make it more uniform and less ill-conditioned, is also used to suppress numerical erros and accelerate convergence. Two criteria, rescaling the maximum of each column to 1 and rescaling the average of each column to 1, were applied and compared to results without rescaling. The results show that, with properly imposed constraints, good quality images can be obtained using the CGD method. The convergence speed is much slower when constraints are imposed, but still comparable to the POCS and SART algorithms. The rescaling technique produces more stable and more accurate reconstructions, and speeds up the reconstruction significantly for all three algorithms.