Research On The Algorithm Of Image Denoising Based On Partial Diffusion Equation And Wavelet Transform

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.