【作者】 赵佰秋；

【导师】 黄凤岗；

【作者基本信息】 哈尔滨工程大学 ， 计算机应用技术， 2007， 硕士

【摘要】 图像降噪是图像处理的重要环节之一，其目的是为了提高图像的信噪比，改善图像质量，尽可能减少噪声对后续图像处理的影响。传统的图像降噪方法主要滤除图像的高频成分，由于图像的细节也分布在高频区域，所以总是在对噪声进行滤除的同时模糊了图像的边缘。小波变换方法与偏微分方程方法是两类重要的降噪方法，本文对基于小波分析和偏微分方程的图像降噪方法分别进行了深入研究，并在此基础上讨论了小波分析和偏微分方程在图像降噪中结合应用的问题。目前，偏微分方程和小波分析在理论上的联系还比较薄弱。本文分析了相干增强扩散方法和小波阈值收缩方法之间的关系，推导了小波收缩方法和相干增强扩散方法之间的一致性，给出了相干增强扩散在小波分析意义下的解释，同时解释了相干增强扩散方法与小波阈值收缩方法在图像性质上的等价性。相干增强扩散方法既能保证边缘的保留也能保证对边缘处的噪声进行处理，而小波变换能够有效提取图像边缘特征，因此文中提出了一种用小波系数估计图像边缘方向的相干增强扩散图像降噪算法，该方法用经过软阈值滤波后的小波系数估计图像边缘方向来构造扩散矩阵，然后对噪声图像用相干增强扩散方法进行降噪处理。仿真试验结果表明文中的扩散算子可以很好地定位和保护图像边缘，较好地运用了小波的时频分析功能，在噪声较大时可以取得较好的降噪效果。更多还原

【Abstract】 Image denoising is one of the most important steps in image processing. Its purpose is to enhance the SNR between original image and de-noised image, improve the character of image, and reduce the influence to the following image processing as far as possible. The traditional methods of image denoising always filter the high-frequency component of image. But the image edges also distribute in high-frequency component. So they are always blurred while filtering the noise in image.Wavelet transform and partial differential equation (PDE) are two important methods of image denoising. In this thesis, firstly, we researched the image denoising based on wavelet transform and PDE separately. Secondly, we discussed the correlation between wavelet transform and PDE in image denoising. Thirdly, we analyzed the relationship between coherence enhancing diffusion (CED) and wavelet shrinkage. Finally, we gave out the interpretation of the CED under wavelet analysis and the equivalency between CED and wavelet shrinkage in image character.CED can not only preserve the image edges but also reduce the noise in image edges. Wavelet transform can effectively extract image edge character. So we proposed an image de-noising algorithm of coherence enhancing diffusion, which used wavelet coefficients to estimate image edge. It used wavelet coefficients, which were shrunk by wavelet soft-shrinkage, to estimate the image edge and then construct diffusion matrix. Finally we reduced the noise in image using CED method. Experimental results showed that the presented diffusion factor could locate and protect image edge accurately, and the presented algorithm could reduce noise effectively.更多还原