首先给出了2维噪声的小波变换特性,分析图像小波变换模的极大值与小波分解级数j和李氏指数之间的关系,指出如何确定和保护图像的边缘;接着阐述了基于软、硬阈值的图像正交小波变换去噪法,然后提出一种基于Neym an-Pearson准则的小波阈值的确定,从而又提出了一种基于小波模极大值和Neym an-Pearson准则阈值的图像去噪方法,解决了图像去噪和保护图像边缘这个“两难”问题。针对期望图像叠加了不规则噪声的假设,对几种去噪方法做了定性比较,并给出了去噪性能的定量分析,仿真结果表明,此方法能提高去噪后图像的信噪比,使评价原图像与去噪后的图像近似程度的方差和相对熵为最小,同时能很好地保留原始图像的边缘信息。

Firstly,this paper gives the property of wavelet transform of two dimensional noise,analyzes the relationship of wavelet transform modulus maxima to different decomposed class j and Lipschitz exponent,and points out how to determine and protect image edges.Then it explains the orthogonal wavelet transform of denoising based on soft and hard threshold,and puts forward a denoising method based on the wavelet modulus maxima and Neyman-Pearson principle. The method finds the optimal trade off between image denoising and protecting image edges.Based on the assumption that the observed image is the sum of the expected image and irregular corruptive noise,the qualitative and quantitative performance of our image denoising method is compared with others.Simulation results show the proposed method can efficiently denoise,such as increasing Signal-to-Noise Ratio(SNR),lowing Mean Square Error(MSE) and Relative Entropy(RE), while preserving the details of the original image.