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A Nonlinear Probabilistic Curvature Motion Filter for Positron Emission Tomography Images

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Scale Space and Variational Methods in Computer Vision (SSVM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5567))

Abstract

Positron Emission Tomography (PET) is an important nuclear medicine imaging technique which enhances the effectiveness of diagnosing many diseases. The raw-projection data, i.e. the sinogram, from which the PET is reconstructed, contains a very high level of Poisson noise. The latter complicates the PET image’s interpretation which may lead to erroneous diagnoses. Suitable denoising techniques prior to reconstruction can significantly alleviate the problem. In this paper, we propose filtering the sinogram with a constraint curvature motion diffusion for which we compute the edge stopping function in terms of edge probability under the assumption of contamination by Poison noise. We demonstrate through simulations with images contaminated by Poisson noise that the performance of the proposed method substantially surpasses that of recently published methods, both visually and in terms of statistical measures.

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References

  1. Chambolle, A.: An Algorithm for Total Variation Minimization and Applications. JMIV 20, 89–97 (2004)

    Article  MathSciNet  Google Scholar 

  2. Chan, T., Li, H., Lysaker, M., Tai, X.C.: Level Set Method for Positron Emission Tomography. International Journal of Biomedical Imaging 2007 (2007)

    Google Scholar 

  3. Comtat, C., Kinahan, P.E., Fessler, J., Beyer, T., Townsend, D.W., Defrise, M., Michel, C.: Clinically feasible reconstruction of 3D whole-body PET/CT data using blurred anatomical labels. Phys. Med. Biol. 47, 1–20 (2002)

    Article  Google Scholar 

  4. Demirkaya, O.: Diffusion Filtering of Functional Images using the structural information available in Hyprid imaging modalities. In: IEEE Medical Imaging Symposium, Germany (2008)

    Google Scholar 

  5. Demirkaya, O.: Post-reconstruction filtering of positron emission tomography whole-body emission images and attenuation maps using nonlinear diffusion filtering. Acad. Radiol. 11, 1105–1114 (2004)

    Article  Google Scholar 

  6. Demirkaya, O.: Anisotropic diffusion filtering of PET attenuation data to improve emission images. Physics in Medicine Biology 47(20), 271–278 (2002)

    Article  Google Scholar 

  7. Didas, S., Weickert, J.: Combining Curvature Motion and Edge-Preserving Denoising. In: Sgallari, F., Murli, A., Paragios, N. (eds.) SSVM 2007. LNCS, vol. 4485, pp. 568–579. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Hudson, M., Larkin, R.: Accelerated image reconstruction using ordered subsets of projection data. IEEE Trans. Med. Imag. 13(4), 601–609 (1994)

    Article  Google Scholar 

  9. Happonen, A.P., Koskinen, M.O.: Experimental Investigation of Angular Stackgram Filtering for Noise Reduction of SPECT Projection Data: Study with Linear and Nonlinear Filters. International Journal of Biomedical Imaging 2007 (2007)

    Google Scholar 

  10. Jonsson, E., Huang, S.C., Chan, T.: Total Variation Regularization in Positron Emission Tomography. UCLA, Tech. Rep. no. 48 (1998)

    Google Scholar 

  11. Kak, C.A., Slaney, M.: Principles of Computerized Tomographic Imaging. IEEE Press, Los Alamitos (1999)

    MATH  Google Scholar 

  12. Nesterov, Y.: Smooth minimization of non-smooth functions. Mathematic Programming, Series A 103, 127–152 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton Jacobi formulations. Journal of Computational Physics 79(1), 12–49 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  14. Padfield, D.R., Manjeshwar, R.: Adaptive conductance filtering for spatially varying noise in PET images. Progress in biomedical optics and imaging 7(3) no. 30 (2006)

    Google Scholar 

  15. Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12, 629–639 (1990)

    Article  Google Scholar 

  16. Pizurica, A., Vanhamel, I., Sahli, H., Philips, W., Katartzis, A.: A Bayesian formulation of edge-stopping functions in non-linear diffusion. IEEE Signal Processing Letters 13(8), 501–504 (2006)

    Article  Google Scholar 

  17. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  18. Rudin, L.I., Osher, S.: Feature-oriented image enhancement with shock filters. Technical Report, Department of Computer Science, California Institute of Technology (1989)

    Google Scholar 

  19. Sapiro, G.: Geometric partial differential equations and image analysis. University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  20. Sumengen, B., Manjunath, B.S.: Edgeflow-driven Variational Image Segmentation: Theory and Performance Evaluation. Technical Report, Department of Electrical and Computer Engineering University of California, Santa Barbara (2006)

    Google Scholar 

  21. Turkheimer, F.E., Boussion, N., Anderson, A.N., Pavese, N., Piccini, P., Visvikis, D.: PET Image Denoising Using a Synergistic Multiresolution Analysis of Structural (MRI/CT) and Functional Datasets. The Journal of nuclear medicine 49, 657–666 (2008)

    Article  Google Scholar 

  22. Vanhamel, I., Mihai, C., Sahli, H., Katartzis, A., Pratikakis, I.: Scale Selection for Compact Scale-Space Representation of Vector-Valued Images. International Journal of Computer Vision 4485 (2008)

    Google Scholar 

  23. Vanhamel, I.: Vector valued nonlinear diffusion and its application to image segmentation Ph.D. Thesis, Vrije Universiteit Brussel, Faculty of Engineering Sciences, Electronics and Informatics (ETRO) (2006)

    Google Scholar 

  24. Wang, Y., Zhou, H.: Total Variation Wavelet-Based Medical Image Denoising. International Journal of Biomedical Imaging 2006 (2006)

    Google Scholar 

  25. Wang, W.: Anisotropic Diffusion Filtering for Reconstruction of Poisson Noisy Sinograms. Journal of Communication and Computer 2(11), 16–23 (2005)

    Google Scholar 

  26. Weickert, J.: Anisotropic diffusion in image processing. ECMI Series. Teubner-Verlag, Stuttgart (1998)

    Google Scholar 

  27. Weiss, P., Aubert, G., Blanc-Fraud, L.: Efficient schemes for total variation minimization under constraints in image processing. Technical Report 6260, INRIA (2007)

    Google Scholar 

  28. Zhu, H., Shu, H., Zhou, J., Bao, X., Luo, L.: Bayesian algorithms for PET image reconstruction with mean curvature and Gauss curvature diffusion regularizations. Computers in Biology and Medicine 37(6), 793–804 (2007)

    Article  Google Scholar 

  29. Zhu, H., Shu, H., Zhou, J., Toumoulin, C., Luo, L.: Image reconstruction for positron emission tomography using fuzzy nonlinear anisotropic diffusion penalty. Med. Biol. Eng. Comput. 44(11), 983–997 (2006)

    Article  Google Scholar 

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Authors and Affiliations

  1. Dept. Electronics and Informatics ETRO-IRIS, Vrije Universiteit Brussel, Pleinlaan 2, B-1050, Brussels, Belgium

    Musa Alrefaya, Hichem Sahli, Iris Vanhamel & Dinh Nho Hao

Authors
  1. Musa Alrefaya
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  2. Hichem Sahli
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  3. Iris Vanhamel
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  4. Dinh Nho Hao
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008, Bergen, Norway

    Xue-Cheng Tai

  2. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Oslo, Norway

    Knut Mørken

  3. Simula Research Laboratory, M. Linges v 17, Fornebu, P.O.Box 134, N-1325, Lysaker, Norway

    Marius Lysaker

  4. SINTEF ICT, Oslo, Norway

    Knut-Andreas Lie

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© 2009 Springer-Verlag Berlin Heidelberg

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Alrefaya, M., Sahli, H., Vanhamel, I., Hao, D.N. (2009). A Nonlinear Probabilistic Curvature Motion Filter for Positron Emission Tomography Images. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_18

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  • DOI: https://doi.org/10.1007/978-3-642-02256-2_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02255-5

  • Online ISBN: 978-3-642-02256-2

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