Abstract
Objective
We propose a statistical stopping criterion for iterative reconstruction in emission tomography based on a heuristic statistical description of the reconstruction process.
Methods
The method was assessed for MLEM reconstruction. Based on Monte-Carlo numerical simulations and using a perfectly modeled system matrix, our method was compared with classical iterative reconstruction followed by low-pass filtering in terms of Euclidian distance to the exact object, noise, and resolution. The stopping criterion was then evaluated with realistic PET data of a Hoffman brain phantom produced using the GATE platform for different count levels.
Results
The numerical experiments showed that compared with the classical method, our technique yielded significant improvement of the noise-resolution tradeoff for a wide range of counting statistics compatible with routine clinical settings. When working with realistic data, the stopping rule allowed a qualitatively and quantitatively efficient determination of the optimal image.
Conclusions
Our method appears to give a reliable estimation of the optimal stopping point for iterative reconstruction. It should thus be of practical interest as it produces images with similar or better quality than classical post-filtered iterative reconstruction with a mastered computation time.
References
Gordon R, Bender R, Herman GT. Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. J Theor Biol. 1970;29:471–81.
Brooks RA, Di Chiro G. Principles of computer assisted tomography (CAT) in radiographic and radioisotopic imaging. Phys Med Biol. 1976;21:689–732.
Goitein M. Three-dimensional density reconstruction from a series of twodimensional projections. Nucl Instrum Methods. 1972;101:509–18.
Gilbert PFC. Iterative methods for the three-dimensional reconstruction of an object from projections. J Theor Biol. 1972;36:105–17.
Xu XL, Liow JS, Strother SC. Iterative algebraic reconstruction algorithms for emission computed tomography: a unified framework and its application to positron emission tomography. Med Phys. 1993;20:1675–84.
Schmidlin P. Iterative separation of sections in tomographic scintigrams. Nucl Med. 1972;11(1):1–16.
Darroch JN, Ratcliff D. Generalized iterative scaling for log-linear models. Ann Math Stat. 1972;43:1470–80.
Dempster A, Laird N, Rubin D. Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc. 1977;39:1–38.
Barrett HH, Swindell W. Radiological imaging—the theory of image formation, detection, and processing. New York: Academic Press; 1981.
Shepp VA, Vardi Y. Maximum likelihood reconstruction for emission tomography. IEEE Trans Med Imaging. 1982;1:113–22.
Byrne CL. Block-iterative methods for image reconstruction from projections. IEEE Trans Image Proc. 1996;5:792–4.
Byrne CL. Accelerating the EMML algorithm and related iterative algorithms by rescaled block-iterative methods. IEEE Trans Image Proc. 1998;7:100–9.
Hudson HM, Larkin RS. Accelerated image reconstruction using ordered subsets of projection data. IEEE Trans Med Imaging. 1994;13:601–9.
Browne J, de Pierro AB. A row-action alternative to the EM algorithm for maximizing likelihood in emission tomography. IEEE Trans Med Imaging. 1996;15:687–99.
Mesina CT, Boellaard R, Jongbloed G, Van der Vaart AW, Lammertsma AA. Experimental evaluation of iterative reconstruction versus filtered backprojection for 3D [15O]water PET activation studies using statistical parametric mapping analysis. Neuroimage. 2003;19:1170–9.
Lubberink M, Boellaard R, Van der Weerdt AP, Visser AC, Lammertsma AA. Quantitative comparison of analytic and iterative reconstruction methods in 2- and 3-dimensional dynamic cardiac 18F-FDG PET. J Nucl Med. 2004;45:2008–15.
Razifar P, Lubberink M, Schneider H, Lâgström B, Bengtsson E, Bergström M. Non-isotropic noise correlation in PET data reconstructed by FBP but not by OSEM demonstrated using auto-correlation function. BMC Med Imaging. 2005;5(1):3.
Liew SC, Hasegawa BH, Brown JK, Lang TF. Noise propagation in SPECT images reconstructed using an iterative maximum likelihood algorithm. Phys Med Biol. 1993;38:1713–27.
Mariano-Goulart D, Fourcade M, Bernon JL, Rossi M, Zanca M. Experimental study of stochastic noise propagation in SPECT images reconstructed using the conjugate gradient algorithm. Comput Med Imaging Graph. 2003;27:53–63.
Hebert TJ. Statistical stopping criteria for iterative maximum likelihood reconstruction of emission images. Phys Med Biol. 1990;35:1221–32.
Snyder DL, Miller MI, Thomas LJ, Politte DG. Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography. IEEE Trans Med Imaging. 1987;6:228–38.
Falcon C, Juvells I, Pavia J, Ros D. Evaluation of a cross-validation stopping rule in MLE SPECT reconstruction. Phys Med Biol. 1998;43:1271–85.
Liang Z, Jaszczak R, Greer K. On Bayesian image reconstruction from projections: uniform and nonuniform a priori source information. IEEE Trans Med Imaging. 1989;8:227–35.
Fessler JA, Hero AO. Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms. IEEE Trans Image Proc. 1995;4:1417–29.
Tanaka E, Kudo H. Subset-dependent relaxation in block-iterative algorithms for image reconstruction in emission tomography. Phys Med Biol. 2003;48:1405–22.
Slijpen ETP, Beekman FJ. Comparison of post-filtering and filtering between iterations for SPECT reconstruction. IEEE Trans Nucl Sci. 1999;46:2233–8.
Knuth DE. Seminumerical algorithms. The art of computer programming, vol 2. Boston: Addison Wesley; 1969.
Jan S et al. for the OpenGATE collaboration, et al. GATE: a simulation toolkit for PET and SPECT. Phys Med Biol. 2004;49:4543–61.
Lamare F, Turzo A, Bizais Y, Le Rest CC, Visvikis D. Validation of a Monte Carlo simulation of the Philips Allegro/GEMINI PET systems using GATE. Phys Med Biol. 2006;51:943–62.
Bailey DL, Meikle SR. A convolution-subtraction scatter correction method for 3D PET. Phys Med Biol. 1994;39:411–24.
Kadrmas DJ. LOR-OSEM: statistical PET reconstruction from raw line-of-response histograms. Phys Med Biol. 2004;49:4731–44.
Acknowledgments
The authors would like to thank I. Buvat and A. Dubois for their technical support regarding the GATE simulations.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ben Bouallègue, F., Crouzet, J.F. & Mariano-Goulart, D. A heuristic statistical stopping rule for iterative reconstruction in emission tomography. Ann Nucl Med 27, 84–95 (2013). https://doi.org/10.1007/s12149-012-0657-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12149-012-0657-5