DOI QR코드

DOI QR Code

Regularization Parameter Selection for Total Variation Model Based on Local Spectral Response

  • Zheng, Yuhui (Jiangsu Engineering Centre of Network Monitoring, College of Computer and Software, Nanjing University of Information Science and Technology) ;
  • Ma, Kai (Jiangsu Engineering Centre of Network Monitoring, College of Computer and Software, Nanjing University of Information Science and Technology) ;
  • Yu, Qiqiong (College of Math and Statistics, Nanjing University of Information Science and Technology) ;
  • Zhang, Jianwei (College of Math and Statistics, Nanjing University of Information Science and Technology) ;
  • Wang, Jin (College of Information Engineering, Yangzhou University)
  • Received : 2017.08.04
  • Accepted : 2017.09.26
  • Published : 2017.10.31

Abstract

In the past decades, various image regularization methods have been introduced. Among them, total variation model has drawn much attention for the reason of its low computational complexity and well-understood mathematical behavior. However, regularization parameter estimation of total variation model is still an open problem. To deal with this problem, a novel adaptive regularization parameter selection scheme is proposed in this paper, by means of using the local spectral response, which has the capability of locally selecting the regularization parameters in a content-aware way and therefore adaptively adjusting the weights between the two terms of the total variation model. Experiment results on simulated and real noisy image show the good performance of our proposed method, in visual improvement and peak signal to noise ratio value.

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. A. Buades, B. Coll, and J. M. Morel, "A review of image denoising algorithms, with a new one," Multiscale Modeling & Simulation, vol. 4, no. 2, pp. 490-530, 2005. https://doi.org/10.1137/040616024
  2. M. Lindenbaum, M. Fischer, and A. Bruckstein, "On Gabor's contribution to image enhancement," Pattern Recognition, vol. 27, no. 1, pp. 1-8, 1994. https://doi.org/10.1016/0031-3203(94)90013-2
  3. E. Hodson, D. Thayer, and C. Franklin, "Adaptive Gaussian filtering and local frequency estimates using local curvature analysis," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 29, no. 4, pp. 854-859, 1981. https://doi.org/10.1109/TASSP.1981.1163641
  4. 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. https://doi.org/10.1109/34.56205
  5. G. Gerig, O. Kubler, R. Kikinis, and F. A. Jolesz, "Nonlinear anisotropic filtering of MRI data," IEEE Transactions on Medical Imaging, vol. 11, no. 2, pp. 221-232, 1992. https://doi.org/10.1109/42.141646
  6. K. Hildebrandt and K. Polthier, "Anisotropic filtering of non-linear surface features," Computer Graphics Forum, vol. 23, no. 3, pp. 391-400, 2010. https://doi.org/10.1111/j.1467-8659.2004.00770.x
  7. L. Alvarez, P. L. Lions, and J. M. Morel, "Image selective smoothing and edge detection by nonlinear diffusion. II," SIAM Journal on Numerical Analysis, vol. 29, no. 3, pp. 845-866, 1992. https://doi.org/10.1137/0729052
  8. L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D: Nonlinear Phenomena, vol. 60, no. 1-4, pp. 259-268, 1992. https://doi.org/10.1016/0167-2789(92)90242-F
  9. J. F. Giovannelli and J. Idier, Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing. Hoboken, NJ: Wiley, 2015.
  10. S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, "An iterative regularization method for total variation-based image restoration," Multiscale Modeling & Simulation, vol. 4, no. 2, pp. 460-489, 2005. https://doi.org/10.1137/040605412
  11. W. Hao and J. Li, "Alternating total variation and non-local total variation for fast compressed sensing magnetic resonance imaging," Electronics Letters, vol. 51, no. 22, pp. 1740-1742, 2015. https://doi.org/10.1049/el.2015.2551
  12. L. P. Yaroslavsky, "Digital picture processing: an introduction," Applied Optics, vol. 25, no. 18, pp. 3127, 1985. https://doi.org/10.1364/AO.25.003127
  13. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. Beijing, China: Publishing House of Electronics Industry, 2011.
  14. M. K. Ozkan, A. T. Erdem, M. I. Sezan, and A. M. Tekalp, "Efficient multiframe Wiener restoration of blurred and noisy image sequences," IEEE Transactions on Image Processing, vol. 1, no. 4, pp. 453-476, 1992. https://doi.org/10.1109/83.199916
  15. S. Citrin and M. R. Azimi-Sadjadi, "A full-plane block Kalman filter for image restoration," IEEE Transactions on Image Processing, vol. 1, no. 4, pp. 488-495, 1992. https://doi.org/10.1109/83.199918
  16. R. Peesapati, S. L. Sabat, K. P. Karthik, J. Nayak, and N. Giribabu, "Efficient hybrid Kalman filter for denoising fiber optic gyroscope signal," Optik-International Journal for Light and Electron Optics, vol. 124, no. 20, pp. 4549-4556, 2013. https://doi.org/10.1016/j.ijleo.2013.02.013
  17. A. Buades, B. Coll, and J. M. Morel, "A non-local algorithm for image denoising," in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CA, 2005, pp. 60-65.
  18. Y. Zheng, J. Zhang, S. Wang, J. Wang, and Y. Chen, "An improved fast nonlocal means filter using patch-oriented 2DPCA," International Journal of Hybrid Information Technology, vol. 5, no. 3, pp. 33-40, 2012.
  19. Z. Yang and M. Jacob, "Nonlocal regularization of inverse problems: a unified variational framework," IEEE Transactions on Image Processing, vol. 22, no. 8, pp. 3192-3203, 2013. https://doi.org/10.1109/TIP.2012.2216278
  20. Y. Lou, X. Zhang, S. Osher, and A. Bertozzi, "Image recovery via nonlocal operators," Journal of Scientific Computing, vol. 42, no. 2, pp. 185-197, 2010. https://doi.org/10.1007/s10915-009-9320-2
  21. B. Xue, Y. Huang, J. Yang, L. Shi, Y. Zhan, and X. Cao, "Fast nonlocal remote sensing image denoising using cosine integral images," IEEE Geoscience and Remote Sensing Letters, vol. 10, no. 6, pp. 1309-1313, 2013. https://doi.org/10.1109/LGRS.2013.2238603
  22. C. Zhang, D. Wu, R. W. Liu, and N. Xiong, "Non-local regularized variational model for image deblurring under mixed Gaussian-impulse noise," Journal of Internet Technology, vol. 16, no. 7, pp. 1301-1319, 2015.
  23. M. Elad, "Why simple shrinkage is still relevant for redundant representations," IEEE Transactions on Information Theory, vol. 52, no. 12, pp. 5559-5569, 2006. https://doi.org/10.1109/TIT.2006.885522
  24. E. Le Pennec and S. Mallat, "Sparse geometric image representations with bandelets," IEEE Transactions on Image Processing, vol. 14, no. 4, pp. 423-438, 2005. https://doi.org/10.1109/TIP.2005.843753
  25. M. Elad and M. Aharon, "Image denoising via sparse and redundant representations over learned dictionaries," IEEE Transactions on Image Processing, vol. 15, no. 12, pp. 3736-3745, 2006. https://doi.org/10.1109/TIP.2006.881969
  26. J. Yang, J. Wright, T. S. Huang, and Y. Ma, "Image super-resolution via sparse representation," IEEE Transactions on Image Processing, vol. 19, no. 11, pp. 2861-2873, 2010. https://doi.org/10.1109/TIP.2010.2050625
  27. T. Peleg, Y. C. Eldar, and M. Elad, "Exploiting statistical dependencies in sparse representations for signal recovery," IEEE Transactions on Signal Processing, vol. 60, no. 5, pp. 2286-2303, 2012. https://doi.org/10.1109/TSP.2012.2188520
  28. J. Ren, J. Liu, and Z. Guo, "Context-aware sparse decomposition for image denoising and superresolution," IEEE Transactions on Image Processing, vol. 22, no. 4, pp. 1456-1469, 2013. https://doi.org/10.1109/TIP.2012.2231690
  29. J. M. Bioucas-Dias and M. A. T. Figueiredo, "A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration," IEEE Transactions on Image Processing, vol. 16, no. 12, pp. 2992-3004, 2007. https://doi.org/10.1109/TIP.2007.909319
  30. Y. Wang, J. Yang, W. Yin, and Y. Zhang, "A new alternating minimization algorithm for total variation image reconstruction," SIAM Journal on Imaging Sciences, vol. 1, no. 3, pp. 248-272, 2008. https://doi.org/10.1137/080724265
  31. J. Yang, Y. Zhang, and W. Yin, "A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data," IEEE Journal of Selected Topics in Signal Processing, vol. 4, no. 2, pp. 288-297, 2010. https://doi.org/10.1109/JSTSP.2010.2042333
  32. K. Chen, E. L. Piccolomini, and F. Zama, "An automatic regularization parameter selection algorithm in the total variation model for image deblurring," Numerical Algorithms, vol. 67, no. 1, pp. 73-92, 2014. https://doi.org/10.1007/s11075-013-9775-y
  33. Y. W. Wen and R. H. Chan, "Parameter selection for total-variation-based image restoration using discrepancy principle," IEEE Transactions on Image Processing, vol. 21, no. 4, pp. 1770-1781, 2012. https://doi.org/10.1109/TIP.2011.2181401
  34. N. P. Galatsanos and A. K. Katsaggelos, "Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation," IEEE Transactions on Image Processing, vol. 1, no. 3, pp. 322-336, 1992. https://doi.org/10.1109/83.148606
  35. Q. Yuan, L. Zhang, H. Shen, and P. Li, "Adaptive multiple-frame image super-resolution based on Ucurve," IEEE Transactions on Image Processing, vol. 19, no. 12, pp. 3157-3170, 2010. https://doi.org/10.1109/TIP.2010.2055571
  36. Y. Zheng, B. Jeon, J. Zhang, and Y. Chen, "Adaptively determining regularisation parameters in nonlocal total variation regularisation for image denoising," Electronics Letters, vol. 51, no. 2, pp. 144-145, 2015. https://doi.org/10.1049/el.2014.3494
  37. V. Estellers, S. Soatto, and X. Bresson, "Adaptive regularization with the structure tensor," IEEE Transactions on Image Processing, vol. 24, no. 6, pp. 1777-1790, 2015. https://doi.org/10.1109/TIP.2015.2409562
  38. G. Gilboa, N. Sochen, and Y. Y. Zeevi, "Variational denoising of partly textured images by spatially varying constraints," IEEE Transactions on Image Processing, vol. 15, no. 8, pp. 2281-2289, 2006. https://doi.org/10.1109/TIP.2006.875247
  39. G. Gilboa, "A total variation spectral framework for scale and texture analysis," SIAM Journal on Imaging Sciences, vol. 7, no. 4, pp. 1937-1961, 2014. https://doi.org/10.1137/130930704
  40. Y. Zheng, M. Li, K. Ma, S. Wang, and J. Wang, "Spectral response based regularization parameter selection for total variation image restoration," in Advanced Multimedia and Ubiquitous Engineering, vol. 448. Singapore: Springer, 2017, pp. 640-645.
  41. J. Zhang, J. Liu, T. Li, Y. Zheng, and J. Wang, "Gaussian mixture model learning based image denoising method with adaptive regularization parameters," Multimedia Tools and Applications, vol. 76, no. 9, pp. 11471-11483, 2017. https://doi.org/10.1007/s11042-016-4214-4
  42. J. Zhang, Q. Yu, Y. Zheng, H. Zhang, and J. Wu, "Regularization parameter selection for TV image denoising using spatially adaptive local spectral response," Journal of Internet Technology, vol. 17, no. 6, pp. 1117-1124, 2016.