Abstract
Emission tomography images are degraded due to the presence of noise and several physical factors, like attenuation and scattering. To remove the attenuation effect from the emission tomography reconstruction, attenuation correction factors (ACFs) are used. These ACFs are obtained from a transmission scan and it is well known that they are homogeneous within each tissue and present abrupt variations in the transition between tissues. In this paper we propose the use of compound Gauss Markov random fields (CGMRF) as prior distributions to model homogeneity within tissues and high variations between regions. In order to find the maximum a posteriori (MAP) estimate of the reconstructed image we propose a new iterative method, which is stochastic for the line process and deterministic for the reconstruction. We apply the ordered subsets (OS) principle to accelerate the image reconstruction. The proposed method is tested and compared with other reconstruction methods.
This work has been partially supported by ”Instituto de Salud Carlos III” projects FIS G03/185, and FIS PI040857 and by the ”Comisión Nacional de Ciencia y Tecnología under contract TIC2003-00880.
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
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bai, C., Kinahan, P.E., Brasse, D., Comtat, C., Townsend, D.W.: Post-injection Single Photon Transmission Tomography with Ordered-Subset Algorithms for Whole-Body PET Imaging. IEEE Tr. Nucl. Sci. 49, 74–81 (2002)
Bouman, C.A., Sauer, K.: A Generalized Gaussian Image Model for Edge-Preserving Map Estimation. IEEE Tr. Im. Proc. 2, 296–310 (1993)
Byrne, C.L.: Accelerating the EMML algorithm and related iterative algorithms by rescaled block-iterative methods. IEEE Tr. Im. Proc. 7, 100–109 (1998)
Erdogan, H., Fessler, J.A.: Monotonic Algorithms for Transmission Tomography. IEEE Tr. Med. Im. 18, 801–814 (1999)
Fessler, J.A.: ASPIRE (A Sparse Precomputed Iterative Reconstruction Library), http://www.eecs.umich.edu/~fessler/aspire/index.html
Geman, S., Geman, G.: Stochastic Relaxation, Gibbs Distributions, and the Bayesian restoration of Images. IEEE Tr. Patt. Anal. Mach. Intell. 6, 721–741 (1984)
Henk, R.E. (ed.): The Scientific Basis of Nuclear Medicine, 2nd edn., Mosby (1996)
Hsiao, I.-T., Rangarajan, A., Khurd, P., Gindi, G.: An Accelerated Convergent Ordered Subsets Algorithm for Emission Tomography. Phys. Med. Biol. 49, 2145–2156 (2004)
Hudson, H.M., Larkin, R.S.: Accelerated Image Reconstruction Using Ordered Subsets of Projection Data. IEEE Tr. Med. Im. 4, 601–609 (1994)
Jeng, F.C., Woods, J.W.: Simulated Annealing in Compound Gaussian Random Fields. IEEE Tr. Inform. Th. 36, 94–107 (1988)
Kak, A.C., Slaney, M.: Principles of Computerized Tomographic Imaging. IEEE Press, Los Alamitos (1988)
Lee, S.-J.: Accelerated Deterministic Annealing Algorithms for Transmission CT Reconstruction Using Ordered Subsets. IEEE Tr. Nucl. Sci. 49, 2373–2380 (2002)
López, A., Molina, R., Mateos, J., Katsaggelos, A.K.: SPECT Image Reconstruction Using Compound Prior Models. Int. J. Pattern Recognit. Artif. Intell. 16, 317–330 (2002)
López, A., Molina, R., Katsaggelos, A.K.: Bayesian Reconstruction for Transmission Tomography with Scale Hyperparameter Estimation. In: Marques, J.S., Pérez de la Blanca, N., Pina, P. (eds.) IbPRIA 2005. LNCS, vol. 3523, pp. 455–462. Springer, Heidelberg (2005)
Molina, R., Katsaggelos, A.K., Mateos, J., Hermoso, A., Segall, C.A.: Restoration of Severely Blurred High Range Images Using Stochastic and Deterministic Relaxation Algorithms in Compound Gauss-Markov Random Fields. Patt. Recogn. 33, 557–571 (2000)
Molina, R., Mateos, J., Katsaggelos, A.K., Vega, M.: Bayesian Multichannel Image Restoration Using Compound Gauss-Markov Random Fields. IEEE Tr. Im. Proc. 12, 1642–1654 (2003)
Oskoui-Fard, P., Stark, H.: Tomographic Image Reconstruction Using the Theory of Convex Projections. IEEE Tr. Med. Im. 7, 45–58 (1988)
Ripley, B.: Spatial Statistic. Wiley, New York (1981)
Takahashi, M., Ogawa, K.: Selection of Projection Set and the Ordered of Calculation in Ordered Subsets Expectation Maximization Method. IEEE Nucl. Scie. Symp. and Med. Imag. Conf. Rec. 2, 1408–1412 (1997)
Urabe, H., Ogawa, K.: Improvement of Reconstructed Images in Ordered Subsets Bayesian Reconstruction Method. IEEE Nucl. Scie. Symp. and Med. Imag. Conf. Rec. 2, 1342–1346 (1998)
Yu, D.F., Fessler, J.A.: Edge-preserving Tomographic Reconstruction with Nonlocal Regularization. IEEE Tr. Med. Im. 21, 159–173 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
López, A., Martín, J.M., Molina, R., Katsaggelos, A.K. (2006). Transmission Tomography Reconstruction Using Compound Gauss-Markov Random Fields and Ordered Subsets. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2006. Lecture Notes in Computer Science, vol 4142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11867661_50
Download citation
DOI: https://doi.org/10.1007/11867661_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44894-5
Online ISBN: 978-3-540-44896-9
eBook Packages: Computer ScienceComputer Science (R0)