Two Modifications of Weight Calculation of the Non-Local Means Denoising Method

Musab Elkheir Salih, Xuming Zhang, Mingyue Ding

School of Life Science and Technology, Huazhong University of Science and Technology, Wuhan, China.

DOI: 10.4236/eng.2013.510B107                

Abstract

The non-local means (NLM) denoising method replaces each pixel by the weighted average of pixels with the sur-rounding neighborhoods. In this paper we employ a cosine weighting function instead of the original exponential func-tion to improve the efficiency of the NLM denoising method. The cosine function outperforms in the high level noise more than low level noise. To increase the performance more in the low level noise we calculate the neighborhood si-milarity weights in a lower-dimensional subspace using singular value decomposition (SVD). Experimental compari-sons between the proposed modifications against the original NLM algorithm demonstrate its superior denoising per-formance in terms of peak signal to noise ratio (PSNR) and histogram, using various test images corrupted by additive white Gaussian noise (AWGN).

Keywords

Non-Local Means; Singular Value Decomposition; Weight Calculation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. Buades, B. Coll and J.-M. Morel, “A Review of Image Denoising Algorithms, with a New One,” SIAM Journal on Multiscale Modeling and Simulation, Vol. 4, No. 2, 2005, pp. 490-530. http://dx.doi.org/10.1137/040616024
[2]	W. Jin, et al., “Fast Non-Local Algorithm for Image Denoising,” 2006 IEEE International Conference on Image Processing, 2006, pp. 1429-1432.
[3]	A. A. Efros and T. K. Leung, “Texture Synthesis by Nonparametric Sampling,” Proceedings of the IEEE International Conference on Computer Vision, Corfu, Greece, September 1999, pp. 1033-1038. http://dx.doi.org/10.1109/ICCV.1999.790383
[4]	Y. Wexler, E. Shechtman and M. Irani, “Space-Time Video Completion,” Proceedings of the IEEE International Conference on Computer Vision Pattern Recognition (CVPR), 2004.
[5]	L. Yatziv, G. Sapiro and M. Levoy, “Light Field Comple- tion,” Proceedings of the IEEE International Conference on Image Processing, Singapore, 2004.
[6]	J. Zeng, et al., “A Matching Method Based on SVD for Image Retrieval,” 2009, pp. 396-398.
[7]	A. Buades, B. Coll and J.-M. Morel, “Nonlocal Image and Movie Denoising,” International Journal of Computer Vision, 2007, to Appear.
[8]	J. Orchard, et al., “Efficient Nonlocal-Means Denoising Using the SVD,” ICIP 2008, 15th IEEE International Conference on Image Processing, 2008, pp. 1732-1735.
[9]	G. Golub and W. Kahan, “Calculating the Singular Values and Pseudo-Inverse of a Matrix,” SIAM Journal on Numerical Analysis, Vol. 2, No. 2, 1965.
[10]	E. Garcia, “SVD and LSI Tutorial 3: Computing the Full SVD of a Matrix,” 2006. http://www.miislita.com/information-retrieval-tutorial/svd-lsitutorial-3-full-svd.html