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**Determining neighborhoods of image pixels automatically for adaptive image denoising using nonlinear time series analysis.**
*(English)*
Zbl 1189.94022

Summary: 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.

### MSC:

94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

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\textit{Z. Liao} et al., Math. Probl. Eng. 2010, Article ID 914564, 14 p. (2010; Zbl 1189.94022)

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