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Inverse Problems and Imaging (IPI)
 

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

Pages: 447 - 467, Volume 9, Issue 2, May 2015      doi:10.3934/ipi.2015.9.447

 
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Daniil Kazantsev - The Manchester X-ray Imaging Facility, School of Materials, The University of Manchester, Manchester, M13 9PL, United Kingdom (email)
William M. Thompson - School of Mathematics, The University of Manchester, Alan Turing Building, Manchester, M13 9PL, United Kingdom (email)
William R. B. Lionheart - School of Mathematics, The University of Manchester, Alan Turing Building, Manchester, M13 9PL, United Kingdom (email)
Geert Van Eyndhoven - iMinds-Vision Lab, The University of Antwerp, Wilrijk, B-2610, Belgium (email)
Anders P. Kaestner - Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut (PSI), Villigen, 5232, Switzerland (email)
Katherine J. Dobson - The Manchester X-ray Imaging Facility, School of Materials, The University of Manchester, Manchester, M13 9PL, United Kingdom (email)
Philip J. Withers - The Manchester X-ray Imaging Facility, School of Materials, The University of Manchester, Manchester, M13 9PL, United Kingdom (email)
Peter D. Lee - The Manchester X-ray Imaging Facility, School of Materials, The University of Manchester, Manchester, M13 9PL, United Kingdom (email)

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.

Keywords:  Time lapse tomography, spatial-temporal penalties, non local means, neutron tomography, GPU acceleration.
Mathematics Subject Classification:  Primary: 65F10, 65F22; Secondary: 62P30.

Received: July 2013;      Revised: April 2014;      Available Online: March 2015.

 References