2-D Kernel Regression Algorithm for Image Denoising

Abstract:

Removing noise from the original image plays an important role in many important applications involving image-based medical diagnosis and visual material examination for public security, and so on. Among them, there have been several published methods to solve the related problem, however, each approach has its advantages, and limitations. This paper examines a new measure of denosing in space domain based on 2-D kernel regression which overcomes the difficulties found in other measures. The idea of this method mainly let the values of a row or a column from an image are taken as the measured results of a fitting function. The following step is to estimate the weight coefficients using least square method. Finally, we obtain an denoised image by resampling the estimated function, and the variable x denotes the coordinate of an image. Results of an experimental applications of this method analysis procedure are given to illustrate the proposed technique, and compared with the basic wavelet-thresholding algorithm for image denoising.

• Periodical: Advanced Materials Research (Volumes 532-533)
• Pages: 1537-1542
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.532-533.1537
• Online since: June 2012
• Authors: Yun Fei Yao, Ye Gang Hu, Chun Sheng Wang, Wei Wei Sun
• Keywords: 2-D Kernel Regression, Image De-Noising, Wavelet Thresholding

References

[1] H. Guo, J. E. Odegard, M. Lang, R. A. Gopinath, I. W. Selesnick, and C. S. Burrus, "Wavelet based speckle reduction with application to SAR based ATD/R", First Int'l Conf. on Image Processing, vol. 1, pp.75-79, Nov. 1994.

DOI: 10.1109/icip.1994.413278

[2] R. D. Nowak, "Wavelet based Rician noise Removal", IEEE Transactions on Image Processing, vol.8, no.10, p.1408, 1999.

DOI: 10.1109/83.791966

[3] D. L. Donoho, "De-noising by soft thresholding", IEEE Trans. Information Theory, vol.41, no.3, pp.613-627, 1995.

DOI: 10.1109/18.382009

[4] S. G. Chang, B. Yu, and M. Vetterli, "Adaptive wavelet thresholding for image denoising and compression", IEEE Trans. Image Processing, vol.9, no.9, pp.1532-1546, 2000.

DOI: 10.1109/83.862633

[5] F. Luisier and T. Blu, "USRE-LET multichannel image denoising: Interscale orthonormal wavelet thresholding", IEEE Trans. Image Processing, vol.17, no.4, pp.482-492, 2008.

DOI: 10.1109/tip.2008.919370

[6] H. Takeda, S. Frsiu, and P. Milanfar, "Kernel regression for image processing and reconstruction", IEEE Trans. Image Processing, vol.16, no.2, pp.349-366, 2007.

DOI: 10.1109/tip.2006.888330

[7] G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., Baltimore: The Johns Hopkins University Press, 1996.

[8] N. K. Bose and N. A. Ahuja, "Supperresolution and noise filtering using moving least squares", IEEE Trans. Image Processing, vol.15, no.8, pp.2239-2248, 2006.

DOI: 10.1109/tip.2006.877406

[9] S. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation", IEEE Trans. Pattern Anal. Machine Intell., vol.11, pp.674-693, July 1989.

DOI: 10.1109/34.192463

[10] R. A. Devore and B. J. Lucier, "Fast wavelet techniques for near-optimal image processing", IEEE Military Communications Conf. Rec. San Diego, vol.3, pp.1129-1135, Oct. 1992.

DOI: 10.1109/milcom.1992.244110

[11] B. Y. Liu. Adaptive training of a kernel-based nonlinear discriminator. Pattern Recognition, vol.38: 2419-2425, 2005.

DOI: 10.1016/j.patcog.2005.03.017

[12] L. Birge, P. Massart, "Estimation of integral functionals of a density", Ann. Statist, vol.23, no.1, pp.11-29, 1995. Figure 2. Comparing the performance of the various methods on lena with sigma = 15. (a)Noisy image, sigma = 15. (b) Hard-threshold. (c) Soft-threshold using Birge-Massart strategy. (d)Half soft-threshold. (e) Generalized wavelet thresholding. (f) Our method .

DOI: 10.1214/aos/1176324452