An Optimal Metric for Regularization Parameter Selection in Iterative Reconstruction for CT Image

Jiayu Duan, Xiaogang Chen, Baiqiang Shen, Xuanqin Mou


Published in:Fully3D 2017 Proceedings


regularization parameter, natural statistics, LoG, pairwise products, statistic features
Regularization parameter selection is crucial in CT iterative reconstruction because it is a balance between fidelity and penalty while there has not been so far a metric to judge if an optimal selection is made which results in the best reconstructed image quality in terms of a well balance between the apparent noise and the image fine structure. In this paper, we proposed a metric for selecting the optimal regularization parameter based on the property of natural image statistics. By using LoG operator and the pairwise products of neighboring LoG signals to extract the statistic features of the reconstructed image to account for the image quality, this proposed method evaluated all selected regularization parameters by calculating the variance of extracted statistic features and picked up the optimal regularization parameter with maximum curve of second order derivation of the calculated variance curve. Numerical and experimental results validated the efficiency of the proposed metric in terms of that the selected regularization parameter is accordance with the best visual observation. Besides, the proposed metric has low complexity of computation and only depends on features, which can be used in multiple situations.

Jiayu Duan
Institute of Image Processing and Pattern Recognition, Xi'an Jiaotong University, China
Xiaogang Chen
Hangzhou power supply company of state grid zhejiang electric power company, China
Baiqiang Shen
Hangzhou power supply company of state grid zhejiang electric power company, China
Xuanqin Mou
Institute of Image Processing and Pattern Recognition, Xi'an Jiaotong University, China
  1. Kunisch, Karl, and J. Zou. "Iterative choices of regularization parameters in linear inverse problems." Inverse Problems14.5(1998):34-40.
  2. Kilmer, Misha E., and D. P. O'Leary. "Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems." Siam Journal on Matrix Analysis & Applications 22.4(2000):1204-1221.
  3. Morozov, V. A. "On the solution of functional equations by the method of regularization." Soviet Math Dokl 7.3(1966):510-512.
  4. G. Golub, M .Heath, and G. Wahba, ”Generalized cross-validation as a method for choosing a good ridge parameter.” Technometrics, vol.21, no. 2,pp. 215-223, 1979
  5. Hansen, By P C. "Analysis of Discrete Ill-Posed Problem by means of L-Curve." Soc. Industr. Appl. Mathem. Rev. 1992 2010.
  6. Lawson C L, Richard J. Hanson "Solving Least Squares Problems[J]. Mathematics of Computation, 1976, 30(135).
  7. Ito, Kazufumi, B. Jin, and T. Takeuchi. "A Regularization Parameter for Nonsmooth Tikhonov Regularization." Siam Journal on Scientific Computing 33.3(2011):1415-1438.
  8. Xuanqin Mou, Ti Bai, Xi Chen, Hengyong Yu, Qingsong Yang and Ge Wang. "Optimal Selection for Regularization Parameter in Iterative CT Reconstruction Based on the Property of Natural Image Statistics."Fully 3D,2015
  9. Xue, W., et al. "Blind Image Quality Assessment Using Joint Statistics of Gradient Magnitude and Laplacian Features." IEEE Transactions on Image Processing 23.11(2014):4850-62.
  10. Noo, F, and M. R. Defrise. "Single-slice rebinning method for helical cone-beam CT. " Physics in Medicine & Biology 44.2(1999):561-57.
  11. Li S C, Paramesran R. Review of medical image quality assessment[J]. Biomedical Signal Processing & Control, 2016, 27:145-154.
  12. Nakhaie A A, Shokouhi S B. No reference medical image quality measurement based on spread spectrum and discrete wavelet transform using ROI processing[J]. 2011, 8069(5):000121-000125.
  13. Dutta J, Ahn S, Li Q. Quantitative Statistical Methods for Image Quality Assessment[J]. Theranostics, 2013, 3(10):741-56.
  14. Lei,Tianhu, Statistics of medical imaging , Boca Raton, FL, 2011. p125-129