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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 732178, 14 pages
http://dx.doi.org/10.1155/2013/732178
Research Article

A Novel Adaptive Probabilistic Nonlinear Denoising Approach for Enhancing PET Data Sinogram

1Department of Electronics and Informatics (ETRO-IRIS), Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
2Faculty of Information Technology and Computer Engineering, Palestine Polytechnic University, Hebron, Palestine
3Interuniversity Microelectronics Centre (IMEC), Leuven, Belgium

Received 23 March 2013; Revised 4 May 2013; Accepted 4 May 2013

Academic Editor: Hang Joon Jo

Copyright © 2013 Musa Alrefaya and Hichem Sahli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629–639, 1990. View at Publisher · View at Google Scholar · View at Scopus
  2. D. Kazantsev, S. R. Arridge, S. Pedemonte et al., “An anatomically driven anisotropic diffusion filtering method for 3D SPECT reconstruction,” Physics in Medicine and Biology, vol. 57, no. 12, pp. 3793–3810, 2012. View at Publisher · View at Google Scholar
  3. Z. Quan and L. Yi, “Image reconstruction algorithm for positron emission tomography with Thin Plate prior combined with an anisotropic diffusion filter,” Journal of Clinical Rehabilitative Tissue Engineering Research, vol. 15, no. 52, 2011.
  4. O. Demirkaya, “Post-reconstruction filtering of positron emission tomography whole-body emission images and attenuation maps using nonlinear diffusion filtering,” Academic Radiology, vol. 11, no. 10, pp. 1105–1114, 2004. View at Publisher · View at Google Scholar · View at Scopus
  5. D. R. Padfield and R. Manjeshwar, “Adaptive conductance filtering for spatially varying noisein PET images,” Progress in Biomedical Optics and Imaging, vol. 7, no. 3, 2006.
  6. J. Weickert, Anisotropic Diffusion in Image Processing, European Consortium for Mathematics in Industry, B. G. Teubner, Stuttgart, Germany, 1998. View at Zentralblatt MATH · View at MathSciNet
  7. M. Alrefaya, H. Sahli, I. Vanhamel, and D. Hao, “A nonlinear probabilistic curvature motion filter for positron emission tomography images,” in Scale Space and Variational Methodsin Computer Vision, vol. 5567 of Lecture Notes in Computer Science, pp. 212–2223, 2009.
  8. O. Demirkaya, “Anisotropic diffusion filtering of PET attenuation data to improve emission images,” Physics in Medicine and Biology, vol. 47, no. 20, pp. N271–N278, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. W. Wang, “Anisotropic diffusion filtering for reconstruction of poisson noisy sinograms,” Journal of Communication and Computer, vol. 2, no. 11, pp. 16–23, 2005.
  10. C. Negoita, R. A. Renaut, and A. Santos, “Nonlinear anisotropic diffusion in positron emission tomography kinetic imaging,” in SIAM Conference on Imaging Science, Salt Lake City, Utah, USA, 2004.
  11. H. Zhu, H. Shu, J. Zhou, C. Toumoulin, and L. Luo, “Image reconstruction for positron emission tomography using fuzzy nonlinear anisotropic diffusion penalty,” Medical and Biological Engineering and Computing, vol. 44, no. 11, pp. 983–997, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Zhu, H. Shu, J. Zhou, X. Bao, and L. Luo, “Bayesian algorithms for PET image reconstruction with mean curvature and Gauss curvature diffusion regularizations,” Computers in Biology and Medicine, vol. 37, no. 6, pp. 793–804, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. A. P. Happonen and M. O. Koskinen, “Experimental investigation of angular stackgram filtering for noise reduction of SPECT projection data: study with linear and nonlinear filters,” International Journal of Biomedical Imaging, vol. 2007, Article ID 38516, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. A. A. Samsonov and C. R. Johnson, “Noise-adaptive nonlinear diffusion filtering of MR images with spatially varying noise levels,” Magnetic Resonance in Medicine, vol. 52, no. 4, pp. 798–806, 2004. View at Publisher · View at Google Scholar · View at Scopus
  15. A. Pizurica, P. Scheunders, and W. Philips, “Multiresolution multispectral image denoisingbased on probability of presence of features of interest,” in Proceedings of Advanced Concepts for Intelligent Vision Systems (Acivs '04), 2004.
  16. I. Vanhamel, Vector valued nonlinear diffusion and its application to image segmentation [Ph.D. thesis], Vrije Universiteit Brussel, Faculty of Engineering Sciences, Electronics and Informatics (ETRO), Brussels, Belgium, 2006.
  17. G. Sapiro, Geometric Partial Differential Equations and Image Analysis, Cambridge University Press, Cambridge, UK, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. A. Kuijper, “Geometrical PDEs based on second-order derivatives of gauge coordinates in image processing,” Image and Vision Computing, vol. 27, no. 8, pp. 1023–1034, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. A. Pižurica, I. Vanhamel, H. Sahli, W. Philips, and A. Katartzis, “A Bayesian formulation of edge-stopping functions in nonlinear diffusion,” IEEE Signal Processing Letters, vol. 13, no. 8, pp. 501–504, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. A. Teymurazyan, T. Riauka, H. S. Jans, and D. Robinson, “Properties of noise in positron emission tomography images reconstructed with filtered-back projection and row-action maximum likelihood algorithm,” Journal of Digital Imaging, vol. 26, no. 3, pp. 447–456, 2013. View at Publisher · View at Google Scholar
  21. G. Miller, H. F. Martz, T. T. Little, and R. Guilmette, “Using exact poisson likelihood functions in Bayesian interpretation of counting measurements,” Health Physics, vol. 83, no. 4, pp. 512–518, 2002. View at Scopus
  22. H. A. Gersch, “Simple formula for the distortions in a Gaussian representation of a Poisson distribution,” American Journal of Physics, vol. 44, no. 9, pp. 885–886, 1976. View at Publisher · View at Google Scholar
  23. J. G. Skellam, “The frequency distribution of the difference between two Poisson variates belonging to different populations,” Journal of the Royal Statistical Society A, vol. 109, no. 3, p. 296, 1946. View at MathSciNet
  24. X. Lei, H. Chen, D. Yao, and G. Luo, “An improved ordered subsets expectation maximization reconstruction,” in Advances in Natural Computation, vol. 4221, pp. 968–971, 2006.
  25. I. Vanhamel, C. Mihai, H. Sahli, A. Katartzis, and I. Pratikakis, “Scale selection for compact scale-space representation of vector-valued images,” International Journal of Computer Vision, vol. 84, no. 2, pp. 194–204, 2009. View at Publisher · View at Google Scholar · View at Scopus
  26. C. Comtat, P. E. Kinahan, J. A. Fessler et al., “Clinically feasible reconstruction of 3D whole-body PET/CT data using blurred anatomical labels,” Physics in Medicine and Biology, vol. 47, no. 1, pp. 1–20, 2002. View at Publisher · View at Google Scholar · View at Scopus
  27. W. J. Niessen, K. L. Vincken, J. A. Weickert, and M. A. Viergever, “Nonlinear multiscale representations for image segmentation,” Computer Vision and Image Understanding, vol. 66, no. 2, pp. 233–245, 1997. View at Scopus