论文标题:图像去噪的偏微分方程方法及其应用
Partial Differential Equation Method and Its Applications for Image Denoising
论文作者 谢华英
论文导师 周海银,论文学位 硕士,论文专业 应用数学
论文单位 国防科学技术大学,点击次数 430,论文页数 55页File Size5804k
2003-11-01论文网 http://www.lw23.com/lunwen_1207182/ 图像去噪;偏微分方程;P-M扩散;相干增强扩散;小波变换
image denoising; partial differential equation(PDE); Perona-Malik diffusion (P-M diffusion); coherence enhancing diffusion(ced); wavelet transform
图像去噪是图像处理中的一个重要问题，对于改善图像质量具有重要的意义。近年来发展起来的偏微分方程方法在去噪的同时能够较好地保持边缘纹理细节，成为人们广泛关注的热点问题。对于常用的两种偏微分方程去噪方法P-M扩散方法和相干增强扩散方法而言，P-M扩散能较好地滤除平坦区域的噪声，但不能有效抑制边缘噪声和保持线状特征，相干增强扩散能有效抑制边缘处噪声但处理相对平坦区域时会出现虚假条纹。基于此，本文提出了两种混合扩散抑制噪声方法： 1、在时域上，本文提出了一种基于边缘检测的混合扩散抑制噪声方法，该方法在图像的边缘部分用相干增强扩散方法进行去噪，其余部分用P-M扩散方法进行去噪。 2、本文还提出了一种基于小波变换的混合扩散抑制噪声方法：先将经小波变换后的噪声图像分频段用不同方法进行去噪处理：低频部分用相干增强扩散方法，高频部分用基于边缘检测的小波阈值法：而后经小波逆变换得到初始去噪图像：再对初始去噪图像用偏微分方程方法作进一步处理，得到最终图像。 同时，本文还从理论上分析了P-M扩散中的参数选择问题，从应用角度出发，分析了相干增强扩散中的参数选取问题，并将其应用于仿真计算。实验结果表明，本文提出的两种方法既可有效去除内区域和边缘处的噪声，又能较好地保持边缘纹理等线状特征，并大大减轻了相干增强扩散过程中产生的虚假条纹现象。
Image denoising is one of the essential topics in image processing, which can greatly improve image quality. Partial differential equation(PDE) technique can keep line-like structures such as edges and textures well while denoising, so it has been focused for recent years. P-M diffusion and coherence enhancing diffusion are two widely used PDE denoising methods. P-M diffusion can remove noise in intra-region sufficiently but cannot eliminate noise at edges successfully and line-like structures cannot be held very well, coherence enhancing diffusion can remove noise at edges and preserve edges very well but false textures arise in intra-region. So, we propose two denoising methods of jointing the two models.Firstly, we develop a jointing diffusion denoising method based on edge detection, that is using coherence enhancing diffusion at the edge of images while using P-M diffusion at the other part.Secondly, we propose a jointing diffusion method of denoising based on wavelet transform. After an image is decomposed by wavelet, denoise the low frequency sub-image by coherence enhancing diffusion and the high frequency sub-images by wavelet threshold denoising method based on edge detection, then an inverse wavelet transform is used to reconstruct the initial denoising image. Next, PDE is used to acquire the final image.Furthermore, we have analyzed how to choose the parameter in P-M diffusion theoretically and how to choose parameters in coherence enhancing diffusion in the aspect of application, then apply them in experiments. Results show that these two methods can reduce noise efficiently in intra-region and at edges, keep line-like structures such as edges and textures better, and reduce artifacts a lot in intra-region in coherence enhancing diffusion.
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