4D-CT reconstruction with unified spatial-temporal patch-based regularization

Daniil Kazantsev; William M. Thompson; William R. B. Lionheart; Geert Van Eyndhoven; Anders P. Kaestner; Katherine J. Dobson; Philip J. Withers; Peter D. Lee

doi:10.3934/ipi.2015.9.447

Article Contents

2015, Volume 9, Issue 2: 447-467. Doi: 10.3934/ipi.2015.9.447 open access

This issue Previous Article Empirical average-case relation between undersampling and sparsity in X-ray CT Next Article Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data

4D-CT reconstruction with unified spatial-temporal patch-based regularization

1.
The Manchester X-ray Imaging Facility, School of Materials, The University of Manchester, Manchester, M13 9PL
2.
School of Mathematics, The University of Manchester, Alan Turing Building, Manchester, M13 9PL
3.
iMinds-Vision Lab, The University of Antwerp, Wilrijk, B-2610
4.
Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut (PSI), Villigen, 5232

Received: June 30, 2013

Revised: March 31, 2014

Published: April 2015

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Abstract

In this paper, we consider a limited data reconstruction problem for temporarily evolving computed tomography (CT), where some regions are static during the whole scan and some are dynamic (intensely or slowly changing). When motion occurs during a tomographic experiment one would like to minimize the number of projections used and reconstruct the image iteratively. To ensure stability of the iterative method spatial and temporal constraints are highly desirable. Here, we present a novel spatial-temporal regularization approach where all time frames are reconstructed collectively as a unified function of space and time. Our method has two main differences from the state-of-the-art spatial-temporal regularization methods. Firstly, all available temporal information is used to improve the spatial resolution of each time frame. Secondly, our method does not treat spatial and temporal penalty terms separately but rather unifies them in one regularization term. Additionally we optimize the temporal smoothing part of the method by considering the non-local patches which are most likely to belong to one intensity class. This modification significantly improves the signal-to-noise ratio of the reconstructed images and reduces computational time. The proposed approach is used in combination with golden ratio sampling of the projection data which allows one to find a better trade-off between temporal and spatial resolution scenarios.

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Mathematics Subject Classification: Primary: 65F10, 65F22; Secondary: 62P30.

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