基于多尺度边缘检测的自适应阈值小波图像降噪

在图像处理中，去除图像中所含噪声而不使其边缘模糊是一个难题。考虑到小波变换在时域和频域均具有良好的局部特性，加之其多分辨率、去相关性等特点，本文提出了一种基于多尺度边缘检测的自适应阈值小波图像降噪方法。该方法将与噪声和边缘相关的小波系数和与同性区域相关的小波系数区别对待。在每个分辨层次，图像的边缘由梯度的幅度来进行估计（梯度的幅度由小波参数导出），且与噪声和边缘有关的梯度的幅度分布由Rayleigh概率模型化。基于此模型，得到该层的收缩函数。为充分利用尺度间相关性，各层的收缩函数被合并起来，进一步保持图像边缘。对与同性区域相关的小波系数，则采用一个基于Bayesian估计的自适应阈值进行处理。实验结果表明，与已有方法相比，该方法不仅可获得较清晰的图像边缘，而且降噪性能优良。

Wavelet image de-noising based on multi-scale edge detection and adaptive threshold

In image processing, removal of noise without blurring the image edges is a difficult problem. Wavelet transform has good localization characteristics in both spatial and spectral domains, and the advantages of de-correlation and multi-resolution. In this paper, a method for image de-noising with multi-scale edge detection and adaptive threshold is proposed. The wavelet coefficients related to noise and edges and the coefficients associated to homogeneous regions are differentiated. At each resolution level, the image edges are estimated by gradient magnitudes (obtained from the wavelet coefficients) whose characteristics are modeled with Rayleigh distribution; and based on this model a shrinkage function is obtained. In order to use the inter-scale dependency, the shrinkage functions are combined to further preserve edges. The wavelet coefficients related to homogeneous regions are processed by an adaptive threshold derived from Bayesian estimation. Experimental results show that comparing with existing methods, this method obtains clearer image edges and better de-noising performance.