Proposal of fault-tolerant tomographic image reconstruction

This paper deals with tomographic image reconstruction under the situation where some of projection data bins are contaminated with abnormal data. Such situations occur in various instances of tomography. We propose a new reconstruction algorithm called the Fault-Tolerant reconstruction outlined as follows. The least-squares (Lnorm) error function ‖ A~x−~b ‖2 used in ordinary iterative reconstructions is sensitive to the existence of abnormal data. The proposed algorithm utilizes the L-norm error function ‖ A~x −~b ‖1 instead of the L -norm, and we develop a row-action-type iterative algorithm using the proximal splitting framework in convex optimization fields. We also propose an improved version of the L-norm reconstruction called the L-TV reconstruction, in which a weak Total Variation (TV) penalty is added to the cost function. Simulation results demonstrate that reconstructed images with the L-norm were severely damaged by the effect of abnormal bins, whereas images with the L-norm and L-TV reconstructions were robust to the existence of abnormal bins.