Abstract
In inverse problems like tomography reconstruction we need to solve an over-determined linear system corrupted with noise. The ML-EM algorithm finds the solution for Poisson noise as the fixed point of iterating a forward projection and a non-linear back projection. In tomography we have several hundred million equations and unknowns. The elements of the huge matrix are high-dimensional integrals, which cannot be stored, but must be re-computed with Monte Carlo (MC) quadrature when needed. In this paper we address the problems of how the quadrature error affects the accuracy of the reconstruction, whether it is possible to modify the back projection to speed up convergence without compromising the accuracy, and whether we should always take the same MC estimate or modify it in every projection.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Buvat, I., Castiglioni, I.: Monte Carlo simulations in SPET and PET. J. Nucl. Med. 46(1), 48–61 (2002)
nanoscan PET/CT. http://www.mediso.com/products.php?fid=2,11&pid=86
Qi, J., Leahy, R.M., Cherry, S.R., Chatziioannou, A., Farquhar, T.H.: High-resolution 3D Bayesian image reconstruction using the microPET small-animal scanner. Phys. Med. Biol. 43(4), 1001 (1998)
Reader, A.J., Zaidi, H.: Advances in PET image reconstruction. PET Clin. 2(2), 173–190 (2007)
Shepp, L., Vardi, Y.: Maximum likelihood reconstruction for emission tomography. IEEE Trans. Med. Imaging 1, 113–122 (1982)
Szirmay-Kalos, L., Magdics, M., Tóth, B., Bükki, T.: Averaging and Metropolis iterations for positron emission tomography. IEEE Trans. Med. Imaging 32(3), 589–600 (2013)
Acknowledgement
This work has been supported by the OTKA K-104476 and by TÁMOP - 4.2.2.B-10/1–2010-0009. The GATE simulation of the Derenzo phantom has been executed by Gergely Patay.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Magdics, M., Szirmay-Kalos, L., Tóth, B., Penzov, A. (2014). Analysis and Control of the Accuracy and Convergence of the ML-EM Iteration. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2013. Lecture Notes in Computer Science(), vol 8353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43880-0_18
Download citation
DOI: https://doi.org/10.1007/978-3-662-43880-0_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-43879-4
Online ISBN: 978-3-662-43880-0
eBook Packages: Computer ScienceComputer Science (R0)