Proposal of fault-tolerant tomographic image reconstruction

TL;DR

This paper introduces a fault-tolerant tomographic image reconstruction algorithm that replaces the traditional L2-norm with an L1-norm to improve robustness against abnormal data, and further enhances it with a TV penalty.

Contribution

It proposes a novel L1-norm based iterative reconstruction algorithm and an improved L1-TV version for robust tomographic imaging in the presence of abnormal data.

Findings

L1-norm reconstruction is robust to abnormal data.

L2-norm reconstruction is severely affected by abnormal bins.

L1-TV reconstruction improves image quality with weak Total Variation penalty.

Abstract

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.