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Mathematical Problems in Engineering
Volume 2016, Article ID 5245948, 13 pages
http://dx.doi.org/10.1155/2016/5245948
Research Article

A Residual-Based Kernel Regression Method for Image Denoising

1College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China
2Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA

Received 7 October 2015; Revised 4 January 2016; Accepted 18 January 2016

Academic Editor: Kacem Chehdi

Copyright © 2016 Jiefei Wang 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. C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of the IEEE 6th International Conference on Computer Vision, pp. 839–846, IEEE, Bombay, India, January 1998. View at Scopus
  2. D. Tschumperlé, PDE's based regularization of multivalued images and applications [Ph.D. thesis], Université de Nice Sophia-Antipolis, Nice, France, 2002.
  3. H. Takeda, S. Farsiu, and P. Milanfar, “Kernel regression for image processing and reconstruction,” IEEE Transactions on Image Processing, vol. 16, no. 2, pp. 349–366, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. E. López-Rubio and M. N. Florentín-Núñez, “Kernel regression based feature extraction for 3D MR image denoising,” Medical Image Analysis, vol. 15, no. 4, pp. 498–513, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. H. Takeda, S. Farsiu, and P. Milanfar, “Higher order bilateral filters and their properties,” in Computational Imaging V, vol. 6498 of Proceedings of SPIE, San Jose, Calif, USA, January 2007. View at Publisher · View at Google Scholar
  6. H. Zhang, J. Yang, Y. Zhang, and T. S. Huang, “Image and video restorations via nonlocal kernel regression,” IEEE Transactions on Cybernetics, vol. 43, no. 3, pp. 1035–1046, 2013. View at Publisher · View at Google Scholar · View at Scopus
  7. H. Zhang, J. Yang, Y. Zhang, and T. S. Huang, “Non-local kernel regression for image and video restoration,” in Computer Vision—ECCV 2010, vol. 6313 of Lecture Notes in Computer Science, pp. 566–579, Springer, Berlin, Germany, 2010. View at Publisher · View at Google Scholar
  8. H. Takeda, S. Farsiu, and P. Milanfar, “Deblurring using regularized locally adaptive kernel regression,” IEEE Transactions on Image Processing, vol. 17, no. 4, pp. 550–563, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. J. Lu, Z. Ye, and Y. Zou, “Huber fractal image coding based on a fitting plane,” IEEE Transactions on Image Processing, vol. 22, no. 1, pp. 134–145, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. H. Takeda, S. Farsiu, and P. Milanfar, “Regularized kernel regression for image deblurring,” in Proceedings of the 40th Asilomar Conference on Signals, Systems, and Computers (ACSSC '06), pp. 1914–1918, Pacific Grove, Calif, USA, November 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. 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 (CVPR '05), pp. 60–65, San Diego, Calif, USA, June 2005. View at Publisher · View at Google Scholar · View at Scopus
  12. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Transactions on Image Processing, vol. 16, no. 8, pp. 2080–2095, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. H. Takeda, P. Milanfar, M. Protter, and M. Elad, “Super-resolution without explicit subpixel motion estimatin,” IEEE Transcations on Image Processing, vol. 18, no. 9, pp. 1958–1975, 2009. View at Publisher · View at Google Scholar
  14. H. Zhang, J. Yang, Y. Zhang, and T. S. Huang, “Multi-scale non-local kernel regression for super resolution,” in Proceedings of the 18th IEEE International Conference on Image Processing (ICIP '11), pp. 1353–1356, IEEE, Brussels, Belgium, September 2011. View at Publisher · View at Google Scholar · View at Scopus
  15. C. Huang, Y. Liang, X. Ding, and C. Fang, “Generalized joint kernel regression and adaptive dictionary learning for single-image super-resolution,” Signal Processing, vol. 103, pp. 142–154, 2014. View at Publisher · View at Google Scholar · View at Scopus
  16. H. Yu, F.-S. Chen, Z.-J. Zhang, and C.-S. Wang, “Single infrared image super-resolution combining non-local means with kernel regression,” Infrared Physics & Technology, vol. 61, pp. 50–59, 2013. View at Publisher · View at Google Scholar · View at Scopus
  17. R. Gallea, E. Ardizzone, R. Pirrone, and O. Gambino, “Three-dimensional fuzzy kernel regression framework for registration of medical volume data,” Pattern Recognition, vol. 46, no. 11, pp. 3000–3016, 2013. View at Publisher · View at Google Scholar · View at Scopus
  18. M. N. Florentín-Núñez, E. López-Rubio, and F. J. López-Rubio, “Adaptive kernel regression and probabilistic self-organizing maps for JPEG image deblocking,” Neurocomputing, vol. 121, pp. 32–39, 2013. View at Publisher · View at Google Scholar · View at Scopus
  19. D. Brunet, E. R. Vrscay, and Z. Wang, “The use of residuals in image denoising,” in Image Analysis and Recognition, M. Kamel and A. Campilho, Eds., vol. 5627 of Lecture Notes in Computer Science, pp. 1–12, Springer, 2009. View at Publisher · View at Google Scholar
  20. M. Zhou, X. Yan, H. Xie, H. Zheng, and G. Yang, “An effective method for signal extraction from residual image, with application to denoising algorithms,” in Advances in Neural Networks—ISNN 2013, vol. 7951 of Lecture Notes in Computer Science, pp. 657–663, Springer, Berlin, Germany, 2013. View at Publisher · View at Google Scholar
  21. T. A. Hearn and L. Reichel, “Image denoising via residual kurtosis minimization,” Numerical Mathematics: Theory, Methods and Applications, vol. 8, no. 3, pp. 406–424, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  22. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600–612, 2004. View at Publisher · View at Google Scholar · View at Scopus
  23. R. L. Euband, Nonparametric Regression and Spline Smoothing, Statistics, Textbooks and Monographs, Marcel Dekker, New York, NY, USA, 2nd edition, 1999.
  24. W. Härdle, Applied Nonparametric Regression, Cambridge University Press, Cambridge, UK, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  25. T. Q. Pham, L. J. Van Vliet, and K. Schutte, “Robust fusion of irregularly sampled data using adaptive normalized convolution,” Eurasip Journal on Applied Signal Processing, vol. 2006, Article ID 083268, 2006. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Elad, “On the origin of the bilateral filter and ways to improve it,” IEEE Transactions on Image Processing, vol. 11, no. 10, pp. 1141–1151, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. D. Barash, “A fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 6, pp. 844–847, 2002. View at Publisher · View at Google Scholar · View at Scopus
  28. R. C. Gonzalez and R. E. Woods, Digital Image Processing, Prentice Hall, 3rd edition, 2007.
  29. M. Kuwahara, K. Hachimura, S. Eiho, and M. Kinoshita, “Processing of RI-angiocardiographic images,” in Digital Processing of Biomedical Images, K. Preston Jr. and M. Onoe, Eds., pp. 187–202, Plenum, New York, NY, USA, 1976. View at Google Scholar
  30. G. Gilboa, N. Sochen, and Y. Y. Zeevi, “Image enhancement and denoising by complex diffusion processes,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 8, pp. 1020–1036, 2004. View at Publisher · View at Google Scholar · View at Scopus
  31. L. Şendur and I. W. Selesnick, “Bivariate shrinkage with local variance estimation,” IEEE Signal Processing Letters, vol. 9, no. 12, pp. 438–441, 2002. View at Publisher · View at Google Scholar · View at Scopus
  32. D. Zhou and W. Cheng, “Image denoising with an optimal threshold and neighbouring window,” Pattern Recognition Letters, vol. 29, no. 11, pp. 1694–1697, 2008. View at Publisher · View at Google Scholar · View at Scopus
  33. F. Luisier, T. Blu, and M. Unser, “A new SURE approach to image denoising: interscale orthonormal wavelet thresholding,” IEEE Transactions on Image Processing, vol. 16, no. 3, pp. 593–606, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. C. A. Micchelli, L. Shen, and Y. Xu, “Proximity algorithms for image models: denoising,” Inverse Problems, vol. 27, no. 4, Article ID 045009, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  35. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Transactions on Image Processing, vol. 16, no. 8, pp. 2080–2095, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus