Copyright © 2012 Shaoxiang Hu et al. 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. D. J. Brenner and E. J. Hall, “Computed tomography—an increasing source of radiation exposure,” New England Journal of Medicine, vol. 357, no. 22, pp. 2277–2284, 2007. View at Publisher · View at Google Scholar · View at Scopus
2. J. Hansen and A. G. Jurik, “Survival and radiation risk in patients obtaining more than six CT examinations during one year,” Acta Oncologica, vol. 48, no. 2, pp. 302–307, 2009. View at Publisher · View at Google Scholar · View at Scopus
3. H. J. Brisse, J. Brenot, N. Pierrat et al., “The relevance of image quality indices for dose optimization in abdominal multi-detector row CT in children: experimental assessment with pediatric phantoms,” Physics in Medicine and Biology, vol. 54, no. 7, pp. 1871–1892, 2009. View at Publisher · View at Google Scholar · View at Scopus
4. L. Yu, “Radiation dose reduction in computed tomography: techniques and future perspective,” Imaging in Medicine, vol. 1, no. 1, pp. 65–84, 2009.
5. J. Weidemann, G. Stamm, M. Galanski, and M. Keberle, “Comparison of the image quality of various fixed and dose modulated protocols for soft tissue neck CT on a GE Lightspeed scanner,” European Journal of Radiology, vol. 69, no. 3, pp. 473–477, 2009. View at Publisher · View at Google Scholar · View at Scopus
6. W. Qi, J. Li, and X. Du, “Method for automatic tube current selection for obtaining a consistent image quality and dose optimization in a cardiac multidetector CT,” Korean Journal of Radiology, vol. 10, no. 6, pp. 568–574, 2009. View at Publisher · View at Google Scholar · View at Scopus
7. A. Kuettner, B. Gehann, J. Spolnik et al., “Strategies for dose-optimized imaging in pediatric cardiac dual source CT,” Rofo, vol. 181, no. 4, pp. 339–348, 2009. View at Publisher · View at Google Scholar · View at Scopus
8. P. Kropil, R. S. Lanzman, C. Walther et al., “Dose reduction and image quality in MDCT of the upper abdomen: potential of an adaptive post-processing filter,” Rofo, vol. 182, no. 3, pp. 248–253, 2009.
9. M. K. Kalra, M. M. Maher, M. A. Blake et al., “Detection and characterization of lesions on low-radiation-dose abdominal CT images postprocessed with noise reduction filters,” Radiology, vol. 232, no. 3, pp. 791–797, 2004. View at Publisher · View at Google Scholar · View at Scopus
10. H. B. Lu, X. Li, L. H. Li et al., “Adaptive noise reduction toward low-dose computed tomography,” in Medical Imaging: Physics of Medical Imaging, vol. 5030 of Proceedings of the SPIE, pp. 759–766, 2003.
11. M. K. Kalra, C. Wittram, M. M. Maher et al., “Can noise reduction filters improve low-radiation-dose chest CT images? Pilot study,” Radiology, vol. 228, no. 1, pp. 257–264, 2003. View at Publisher · View at Google Scholar · View at Scopus
12. M. K. Kalra, M. M. Maher, D. V. Sahani et al., “Low-dose CT of the abdomen: evaluation of image improvement with use of noise reduction filters—Pilot study,” Radiology, vol. 228, no. 1, pp. 251–256, 2003. View at Publisher · View at Google Scholar · View at Scopus
13. J. C. Ramirez Giraldo, Z. S. Kelm, L. S. Guimaraes et al., “Comparative study of two image space noise reduction methods for computed tomography: bilateral filter and nonlocal means,” in Proceedings of the 31st Annual International Conference of the IEEE Engineering in Medicine and Biology Society: Engineering the Future of Biomedicine (EMBC '09), pp. 3529–3532, September 2009. View at Publisher · View at Google Scholar · View at Scopus
14. A. Manduca, L. Yu, J. D. Trzasko et al., “Projection space denoising with bilateral filtering and CT noise modeling for dose reduction in CT,” Medical Physics, vol. 36, no. 11, pp. 4911–4919, 2009. View at Publisher · View at Google Scholar · View at Scopus
15. N. Mail, D. J. Moseley, J. H. Siewerdsen, and D. A. Jaffray, “The influence of bowtie filtration on cone-beam CT image quality,” Medical Physics, vol. 36, no. 1, pp. 22–32, 2009. View at Publisher · View at Google Scholar · View at Scopus
16. M. Kachelrieß, O. Watzke, and W. A. Kalender, “Generalized multi-dimensional adaptive filtering for conventional and spiral single-slice, multi-slice, and cone-beam CT,” Medical Physics, vol. 28, no. 4, pp. 475–490, 2001. View at Publisher · View at Google Scholar · View at Scopus
17. G. F. Rust, V. Aurich, and M. Reiser, “Noise/dose reduction and image improvements in screening virtual colonoscopy with tube currents of 20 mAs with nonlinear Gaussian filter chains,” in Medical Imaging: Physiology and Function from Multidimensional Images, vol. 4683 of Proceedings of the SPIE, pp. 186–197, San Diego, Calif, USA, February 2002. View at Publisher · View at Google Scholar · View at Scopus
18. Z. Liao, S. Hu, and W. Chen, “Determining neighborhoods of image pixels automatically for adaptive image denoising using nonlinear time series analysis,” Mathematical Problems in Engineering, vol. 2010, Article ID 914564, 14 pages, 2010. View at Publisher · View at Google Scholar
19. H.-C. Hsin, T.-Y. Sung, and Y.-S. Shieh, “An adaptive coding pass scanning algorithm for optimal rate control in biomedical images,” Computational and Mathematical Methods in Medicine, vol. 2012, Article ID 935914, 7 pages, 2012. View at Publisher · View at Google Scholar
20. H. Lu, I. T. Hsiao, X. Li, and Z. Liang, “Noise properties of low-dose CT projections and noise treatment by scale transformations,” in Proceedings of the IEEE Nuclear Science Symposium Conference Record, vol. 1–4, pp. 1662–1666, November 2001. View at Scopus
21. J. Xu and B. M. W. Tsui, “Electronic noise modeling in statistical iterative reconstruction,” IEEE Transactions on Image Processing, vol. 18, no. 6, pp. 1228–1238, 2009. View at Publisher · View at Google Scholar · View at Scopus
22. I. A. Elbakri and J. A. Fessler, “Statistical image reconstruction for polyenergetic X-ray computed tomography,” IEEE Transactions on Medical Imaging, vol. 21, no. 2, pp. 89–99, 2002. View at Publisher · View at Google Scholar · View at Scopus
23. P. J. La Rivière and D. M. Billmire, “Reduction of noise-induced streak artifacts in X-ray computed tomography through spline-based penalized-likelihood sinogram smoothing,” IEEE Transactions on Medical Imaging, vol. 24, no. 1, pp. 105–111, 2005. View at Publisher · View at Google Scholar · View at Scopus
24. P. J. La Rivière, “Penalized-likelihood sinogram smoothing for low-dose CT,” Medical Physics, vol. 32, no. 6, pp. 1676–1683, 2005. View at Publisher · View at Google Scholar · View at Scopus
25. J. Wang, H. Lu, J. Wen, and Z. Liang, “Multiscale penalized weighted least-squares sinogram restoration for low-dose X-ray computed tomography,” IEEE Transactions on Biomedical Engineering, vol. 55, no. 3, pp. 1022–1031, 2008. View at Publisher · View at Google Scholar · View at Scopus
26. P. Forthmann, T. Köhler, P. G. C. Begemann, and M. Defrise, “Penalized maximum-likelihood sinogram restoration for dual focal spot computed tomography,” Physics in Medicine and Biology, vol. 52, no. 15, pp. 4513–4523, 2007. View at Publisher · View at Google Scholar · View at Scopus
27. J. Wang, T. Li, H. Lu, and Z. Liang, “Penalized weighted least-squares approach to sinogram noise reduction and image reconstruction for low-dose X-ray computed tomography,” IEEE Transactions on Medical Imaging, vol. 25, no. 10, pp. 1272–1283, 2006. View at Publisher · View at Google Scholar · View at Scopus
28. Z. Liao, S. Hu, M. Li, and W. Chen, “Noise estimation for single- slice sinogram of low-dose X-ray computed tomography using homogenous patch,” Mathematical Problems in Engineering, vol. 2012, Article ID 696212, 16 pages, 2012. View at Publisher · View at Google Scholar
29. H. B. Lu, X. Li, I. T. Hsiao, and Z. G. Liang, “Analytical noise treatment for low-dose CT projection data by penalized weighted least-square smoothing in the K-L domain,” in Medical Imaging: Physics of Medical Imaging, vol. 4682 of Proceedings of the SPIE, pp. 146–152, 2002.
30. 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
31. A. M. Mendrik, E. J. Vonken, A. Rutten, M. A. Viergever, and B. Van Ginneken, “Noise reduction in computed tomography scans using 3-D anisotropic hybrid diffusion with continuous switch,” IEEE Transactions on Medical Imaging, vol. 28, no. 10, pp. 1585–1594, 2009. View at Publisher · View at Google Scholar · View at Scopus
32. T. S. Kim, C. Huang, J. W. Jeong, D. C. Shin, M. Singh, and V. Z. Marmarelis, “Sinogram enhancement for high-resolution ultrasonic transmission tomography using nonlinear anisotropic coherence diffusion,” in Proceedings of the IEEE Ultrasonics Symposium, vol. 1, pp. 1816–1819, October 2003. View at Scopus
33. M. Ceccarelli, V. De Simone, and A. Murli, “Well-posed anisotropic diffusion for image denoising,” IEE Proceedings, vol. 149, no. 4, pp. 244–252, 2002. View at Publisher · View at Google Scholar · View at Scopus
34. V. B. Surya Prasath and A. Singh, “Well-posed inhomogeneous nonlinear diffusion scheme for digital image denoising,” Journal of Applied Mathematics, vol. 2010, Article ID 763847, 14 pages, 2010. View at Publisher · View at Google Scholar
35. Z. Liao, S. Hu, D. Sun, and W. Chen, “Enclosed laplacian operator of nonlinear anisotropic diffusion to preserve singularities and delete isolated points in image smoothing,” Mathematical Problems in Engineering, vol. 2011, Article ID 749456, 15 pages, 2011. View at Publisher · View at Google Scholar
36. T. Li, X. Li, J. Wang et al., “Nonlinear sinogram smoothing for low-dose X-ray CT,” IEEE Transactions on Nuclear Science, vol. 51, no. 5, pp. 2505–2513, 2004. View at Publisher · View at Google Scholar · View at Scopus
37. S. Hu, Zh. Liao, D. Sun, and W. Chen, “A numerical method for preserving curve edges in nonlinear anisotropic smoothing,” Mathematical Problems in Engineering, vol. 2011, Article ID 186507, 14 pages, 2011. View at Publisher · View at Google Scholar
38. Y. L. You and M. Kaveh, “Fourth-order partial differential equations for noise removal,” IEEE Transactions on Image Processing, vol. 9, no. 10, pp. 1723–1730, 2000. View at Publisher · View at Google Scholar · View at Scopus
39. Y. Zhang, H. D. Cheng, Y. Q. Chen, and J. Huang, “A novel noise removal method based on fractional anisotropic diffusion and subpixel approach,” New Mathematics and Natural Computation, vol. 7, no. 1, pp. 173–185, 2011. View at Publisher · View at Google Scholar
40. D. Chen, Y. Q. Chen, and D. Xue, “Digital fractional order Savitzky-Golay differentiator and its application,” in Proceedings of the ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE '11), Washington, DC, USA, August 2011.
41. L.-T. Ko, J.-E. Chen, Y.-S. Shieh, M. Scalia, and T.-Y. Sung, “A novel fractional discrete cosine transform based reversible watermarking for healthcare information management systems,” Mathematical Problems in Engineering, vol. 2012, Article ID 757018, 2012. View at Publisher · View at Google Scholar
42. T. F. Chan, S. Esedoglu, and F. Park, “A fourth order dual method for staircase reduction in texture extraction and image restoration problems,” in Proceedings of the 17th IEEE International Conference on Image Processing (ICIP '10), pp. 4137–4140, September 2010. View at Publisher · View at Google Scholar · View at Scopus
43. T. Chan, A. Marquina, and P. Mulet, “High-order total variation-based image restoration,” SIAM Journal on Scientific Computing, vol. 22, no. 2, pp. 503–516, 2001. View at Publisher · View at Google Scholar · View at Scopus
44. Z. Jun and W. Zhihui, “A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising,” Applied Mathematical Modelling, vol. 35, no. 5, pp. 2516–2528, 2011. View at Publisher · View at Google Scholar · View at Scopus
45. M. Li and W. Zhao, “Visiting power laws in cyber-physical networking systems,” Mathematical Problems in Engineering, vol. 2012, Article ID 302786, 13 pages, 2012. View at Publisher · View at Google Scholar
46. M. Li, C. Cattani, and S. Y. Chen, “Viewing sea level by a one-dimensional random function with long memory,” Mathematical Problems in Engineering, vol. 2011, Article ID 654284, 2011. View at Publisher · View at Google Scholar · View at Scopus
47. M. Li, “Fractal time series-a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 2010. View at Publisher · View at Google Scholar · View at Scopus
48. Y. F. Pu, “Application of fractional differential approach to digital image processing,” Journal of Sichuan University, vol. 39, no. 3, pp. 124–132, 2007. View at Scopus
49. J. Bai and X. C. Feng, “Fractional-order anisotropic diffusion for image denoising,” IEEE Transactions on Image Processing, vol. 16, no. 10, pp. 2492–2502, 2007. View at Publisher · View at Google Scholar · View at Scopus
50. 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
51. Y. Chen, W. Chen, X. Yin et al., “Improving low-dose abdominal CT images by Weighted Intensity Averaging over Large-scale Neighborhoods,” European Journal of Radiology, vol. 80, no. 2, pp. e42–e49, 2011. View at Publisher · View at Google Scholar · View at Scopus