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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 732178, 14 pages
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- J. Weickert, Anisotropic Diffusion in Image Processing, European Consortium for Mathematics in Industry, B. G. Teubner, Stuttgart, Germany, 1998.
- 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.
- 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.
- W. Wang, “Anisotropic diffusion filtering for reconstruction of poisson noisy sinograms,” Journal of Communication and Computer, vol. 2, no. 11, pp. 16–23, 2005.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- G. Sapiro, Geometric Partial Differential Equations and Image Analysis, Cambridge University Press, Cambridge, UK, 2001.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.