Abstract
We propose an hyper-parameter inference method in the manner of Bayesian inference for image reconstruction from Radon transformed observation which often appears in the computed tomography. Hyper-parameters are often introduced in Bayesian inference to control the strength ratio between prior information and the fidelity to the observation. Since the quality of the reconstructed image is influenced by the estimation accuracy of these hyper-parameters, we apply Bayesian inference into the filtered back projection (FBP) reconstruction method with hyper-parameters inference, and demonstrate that estimated hyper-parameters can adapt to the noise level in the observation automatically.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ramachandran, G.N., Lakshminarayanan, A.V.: Three-dimensional reconstruction from radiographs and electron micrographs. Proceedings of the National Academy of Sciences of the United States of America 68, 2236–2240 (1971)
Shepp, L.A., Logan, B.F.: Reconstructing interior head tissue from x-ray transmissions. IEEE Trans. Nucl. Sci. 21, 228–236 (1974)
Shepp, L.A., Vardi, Y.: Maximum likelihood reconstrction for emission tomography. IEEE Transactions on Medical Imaging 1, 113–122 (1982)
Green, P.J.: Bayesian reconstructions from emission tomography data using a modified em algorithm. IEEE Transactions on Medical Imaging 9, 84–93 (1990)
Geman, S., Geman, D.: Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721–741 (1984)
Pryce, J.M., Bruce, A.D.: Statistical mechanics of image restoration. Journal of Physics A: Mathematical and General 28, 511–532 (1995)
Mackay, D.J.C., Laboratory, C.: Hyperparameters: optimize, or integrate out. In: Maximum Entropy and Bayesian Methods, Santa Barbara, pp. 43–60. Kluwer, Dordrecht (1996)
Mackay, D.J.C.: Information Theory, Inference and Learning Algorithm. Cambridge University Press, Cambridge (2003)
Inoue, J., Tanaka, K.: Dynamics of maximum marginal likelihood hyper-parameter estimation in image restoration: Gradient descent vs. em algorithm. Physical Review E 65(1), 016125–1 – 016125–11 (2002)
Tanaka, K.: Statistical-mechanical approach to image processing. Journal of Physics A: Mathematical and General 35(37), R81–R150 (2002)
Tanaka, K., Shouno, H., Okada, M., Titterington, D.M.: Accuracy of the bethe approximation for hyperparameter estimation in probabilistic image processing. Journal of Physics A: Mathematical and General 37, 8675–8695 (2004)
R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2009) ISBN 3-900051-07-0
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shouno, H., Okada, M. (2010). A Hyper-parameter Inference for Radon Transformed Image Reconstruction Using Bayesian Inference . In: Wang, F., Yan, P., Suzuki, K., Shen, D. (eds) Machine Learning in Medical Imaging. MLMI 2010. Lecture Notes in Computer Science, vol 6357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15948-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-15948-0_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15947-3
Online ISBN: 978-3-642-15948-0
eBook Packages: Computer ScienceComputer Science (R0)