Proposal of fault-tolerant tomographic image reconstruction
This addresses the problem of reliable image reconstruction in tomography for applications where data contamination occurs, representing an incremental improvement over existing methods.
The paper tackles tomographic image reconstruction when projection data contains abnormal bins, proposing a fault-tolerant algorithm using L1-norm error and L1-TV reconstruction to improve robustness. Simulation results show that L2-norm reconstructions are severely damaged by abnormal data, while the proposed methods remain robust.
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 (L2-norm) error function ||Ax-b||_2^2 used in ordinary iterative reconstructions is sensitive to the existence of abnormal data. The proposed algorithm utilizes the L1-norm error function ||Ax-b||_1^1 instead of the L2-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 L1-norm reconstruction called the L1-TV reconstruction, in which a weak Total Variation (TV) penalty is added to the cost function. Simulation results demonstrate that reconstructed images with the L2-norm were severely damaged by the effect of abnormal bins, whereas images with the L1-norm and L1-TV reconstructions were robust to the existence of abnormal bins.