Total variation regularization in measurement and image space for PET reconstruction

Burger, M; Müller, J. D.; Papoutsellis, E; Schönlieb, C B

Total variation regularization in measurement and image space for PET reconstruction

Type

Article

Authors

Burger, M
Müller, J. D.

Papoutsellis, E
Schönlieb, C B

KAUST Grant Number

KUK-I1-007-43

Online Publication Date

2014-09-18

Print Publication Date

2014-10-01

Date

2014-09-18

Abstract

© 2014 IOP Publishing Ltd. The aim of this paper is to test and analyse a novel technique for image reconstruction in positron emission tomography, which is based on (total variation) regularization on both the image space and the projection space. We formulate our variational problem considering both total variation penalty terms on the image and on an idealized sinogram to be reconstructed from a given Poisson distributed noisy sinogram. We prove existence, uniqueness and stability results for the proposed model and provide some analytical insight into the structures favoured by joint regularization. For the numerical solution of the corresponding discretized problem we employ the split Bregman algorithm and extensively test the approach in comparison to standard total variation regularization on the image. The numerical results show that an additional penalty on the sinogram performs better on reconstructing images with thin structures.

Citation

Burger M, Müller J, Papoutsellis E, Schönlieb CB (2014) Total variation regularization in measurement and image space for PET reconstruction. Inverse Problems 30: 105003. Available: http://dx.doi.org/10.1088/0266-5611/30/10/105003.

Acknowledgements

This work has been financially supported by the King Abdullah University of Science and Technology (KAUST) Award No. KUK-I1-007-43, the EPSRC first grant EP/J009539/1, the Royal Society International Exchange Award Nr. IE110314, and the German Science Foundation (DFG) through the Collaborative Research Centre SFB 656 subproject B2 and Cells-in-Motion Cluster of Excellence (EXC 1003 CiM), University of Munster.