Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 914564, 14 pages
doi:10.1155/2010/914564
Research Article

Determining Neighborhoods of Image Pixels Automatically for Adaptive Image Denoising Using Nonlinear Time Series Analysis

Zhiwu Liao,1 Shaoxiang Hu,2 and Wufan Chen3

1Key Laboratory of Land Resources Evaluation and Monitoring of Southwest, Sichuan Normal University, Ministry of Education, Chengdu 610068, Sichuan, China
2School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, Sichuan, China
3Institute of Medical Information and Technology, School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China

Received 30 January 2010; Accepted 20 March 2010

Academic Editor: Ming Li

Copyright © 2010 Zhiwu Liao 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.

Abstract

This paper presents a method determining neighborhoods of the image pixels automatically in adaptive denoising. The neighborhood is named stationary neighborhood (SN). In this method, the noisy image is considered as an observation of a nonlinear time series (NTS). Image denoising must recover the true state of the NTS from the observation. At first, the false neighbors (FNs) in a neighborhood for each pixel are removed according to the context. After moving the FNs, we obtain an SN, where the NTS is stationary and the real state can be estimated using the theory of stationary time series (STS). Since each SN of an image pixel consists of elements with similar context and nearby locations, the method proposed in this paper can not only adaptively find neighbors and determine size of the SN according to the characteristics of a pixel, but also be able to denoise while effectively preserving edges. Finally, in order to show the superiority of this algorithm, we compare this method with the existing universal denoising algorithms.