Proposal of fault-tolerant tomographic image reconstruction

Hiroyuki Kudo; Keita Takaki; Fukashi Yamazaki; Takuya Nemoto

doi:10.1117/12.2237107

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||²₂ used in ordinary iterative reconstructions is sensitive to the existence of abnormal data. The proposed algorithm utilizes the L¹-norm error function || Ax- b||¹₁ 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.

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Citation Download Citation

Hiroyuki Kudo, Hiroyuki Kudo, Keita Takaki, Keita Takaki, Fukashi Yamazaki, Fukashi Yamazaki, Takuya Nemoto, Takuya Nemoto, } "Proposal of fault-tolerant tomographic image reconstruction", Proc. SPIE 9967, Developments in X-Ray Tomography X, 99671K (3 October 2016); doi: 10.1117/12.2237107; https://doi.org/10.1117/12.2237107

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