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Mathematical Problems in Engineering
Volume 2015, Article ID 340182, 9 pages
Research Article

Image Denoising via Asymptotic Nonlocal Filtering

1School of Mathematics and Statistics, Xidian University, Xi’an 710071, China
2School of Science, Xi’an Shiyou University, 18 Second Dianzi Road, Yanta District, Xi’an, Shaanxi 710065, China
3School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China

Received 6 February 2014; Revised 5 October 2014; Accepted 7 October 2014

Academic Editor: Dan Simon

Copyright © 2015 Xiaoyan Liu 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.


The nonlocal means algorithm is widely used in image denoising, but this algorithm does not work well for high-intensity noise. To overcome this shortcoming, we establish a coupled iterative nonlocal means model in this paper. Considering the computation complexity of the new model, we realize it by using multiscale wavelet transform and propose an asymptotic nonlocal filtering algorithm which can reduce the influence of noise on similarity estimation and computation complexity. Moreover, we build a new nonlocal weight function based on the structure similarity index. Simulation results indicate that the proposed approach cannot only remove the noise but also preserve the structure of image and has good visual effects, especially for highly degenerated images.