Sinogram restoration for low-dosed \(X\)-ray computed tomography using fractional-order Perona-Malik diffusion.

*(English)*Zbl 1264.94015Summary: Existing integer-order nonlinear anisotropic diffusion (NAD) used in noise suppressing will produce undesirable staircase effect or speckle effect. In this paper, we propose a new scheme, named fractal-order Perona-Malik diffusion (FPMD), which replaces the integer-order derivative of the Perona-Malik (PM) diffusion with the fractional-order derivative using G-L fractional derivative. FPMD, which is a interpolation between integer-order NAD and fourth-order partial differential equations, provides a more flexible way to balance the noise reducing and anatomical details preserving. Smoothing results for phantoms and real sinograms show that FPMD with suitable parameters can suppress the staircase effects and speckle effects efficiently. In addition, FPMD also has a good performance in visual quality and root mean square errors (RMSE).

##### MSC:

94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |

35R30 | Inverse problems for PDEs |

35R11 | Fractional partial differential equations |

92C55 | Biomedical imaging and signal processing |

35K10 | Second-order parabolic equations |

PDF
BibTeX
XML
Cite

\textit{S. Hu} et al., Math. Probl. Eng. 2012, Article ID 391050, 13 p. (2012; Zbl 1264.94015)

Full Text:
DOI

**OpenURL**

##### 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. |

[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. |

[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. |

[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. |

[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. |

[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. |

[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. |

[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. |

[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. |

[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. |

[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. |

[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. |

[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. |

[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. |

[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. · Zbl 1189.94022 |

[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. · Zbl 1227.92037 |

[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. |

[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. · Zbl 1371.94419 |

[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. |

[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. |

[24] | P. J. La Rivière, “Penalized-likelihood sinogram smoothing for low-dose CT,” Medical Physics, vol. 32, no. 6, pp. 1676-1683, 2005. |

[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. |

[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. |

[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. |

[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. · Zbl 06173491 |

[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. · Zbl 05111848 |

[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. |

[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. |

[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. |

[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. · Zbl 1189.94024 |

[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. · Zbl 1213.94019 |

[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. |

[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. · Zbl 1213.76040 |

[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. · Zbl 0962.94011 |

[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. · Zbl 1216.65032 |

[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. · Zbl 06173552 |

[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. |

[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. · Zbl 0968.68175 |

[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. · Zbl 1217.94024 |

[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. · Zbl 06173174 |

[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. · Zbl 05829261 |

[47] | M. Li, “Fractal time series-a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 2010. · Zbl 1191.37002 |

[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. |

[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. · Zbl 05453693 |

[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. · Zbl 05111848 |

[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. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.