Fast binary CT using Fourier null space regularization (FNSR)
File(s)
Accepted version
Author(s)
Jones, GA
Huthwaite, P
Type
Journal Article
Abstract
X-ray CT is increasingly being adopted in manufacturing as a non destructive inspection tool. Traditionally, industrial workflows follow a two step procedure of reconstruction followed by segmentation. Such workflows suffer from two main problems: (1) the reconstruction typically requires thousands of projections leading to increased data acquisition times. (2) The application of the segmentation process a posteriori is dependent on the quality of the original reconstruction and often does not preserve data fidelity. We present a fast iterative x-ray CT method which simultaneously reconstructs and segments an image from a limited number of projections called Fourier null space regularization (FNSR). The novelty of the approach is in the explicit updating of the image null space with values derived from a regularized image from the previous iteration, thus compensating for any missing projections and effectively regularizing the reconstruction. The speed of the method is achieved by directly applying the Fourier Slice Theorem where the non-uniform fast Fourier transform (NUFFT) is used to compute the frequency spectrum of the projections at their positions in the image k-space. At each iteration a segmented image is computed which is used to populate the null values of the image k-space effectively steering the reconstruction towards a binary solution. The effectiveness of the method to generate accurate reconstructions is demonstrated and benchmarked against other iterative reconstruction techniques using a series of numerical examples. Finally, FNSR is validated using industrial x-ray CT data where accurate reconstructions were achieved with 18 or more projections, a significant reduction from the 5000 needed by filtered back projection.
Date Issued
2020-03-01
Date Acceptance
2019-10-18
Citation
Inverse Problems, 2020, 36 (3)
ISSN
0266-5611
Publisher
IOP Publishing
Journal / Book Title
Inverse Problems
Volume
36
Issue
3
Copyright Statement
© 2020 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication inInverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at https://iopscience.iop.org/article/10.1088/1361-6420/ab4f4e
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000537451000002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/L022125/1
EP/M020207/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Physics, Mathematical
Mathematics
Physics
binary tomography
CT reconstruction
null space regularization
non uniform FFT
imaging
X-RAY TOMOGRAPHY
IMAGE-RECONSTRUCTION
ALGORITHM
SEGMENTATION
Publication Status
Published
Article Number
ARTN 035019
Date Publish Online
2020-02-14