【作者】 丛丽丽；

【导师】 马驷良；

【作者基本信息】 吉林大学 ， 计算数学， 2010， 硕士

【摘要】 近年来,图像去噪问题一直都是国内外研究者所关注的研究课题,因为噪声去除的好坏,直接影响着图像的质量、视觉效果以及后续更高层次处理的需要.而图像去噪过程中,面临的关键问题是在抑制噪声的同时,如何更好地保护图像的重要细节特征.小波包分析技术和偏微分方程方法是图像去噪中两种比较有效的方法.本文对小波包分析方法和基于全变差的去噪方法进行了深入的研究和总结,根据它们各自的去噪特点,提出了一种新的去噪算法,即基于小波包和全变差的图像去噪算法.首先利用小波包变换的多分辨分析,对含噪图像进行四层分解；其次根据选定的信息代价函数来选取最优小波包基；再次对被选取的最优小波包基下的小波包系数进行阈值化处理,利用处理后的系数重构图像；最后采用全变差的方法,将初步处理的图像进行进一步去噪.数值实验表明本文的方法不仅提高了图像的峰值信噪比(PSNR)值而且获得了令人比较满意的视觉效果,因而证明了本文方法的可行性和有效性.更多还原

【Abstract】 Image Denoising Algorithm Based On Wavelet Packet And Total VariationImage is contaminated by different levels of noise produced in image acquisi-tion, transformation and storage,which makes image blurred.It not only undermines the image quality and applied results,but also affects the follow-up deep-level image processing.In order to improve image quality and the need for follow-up deep-level processing, image denoising has become an essential task in image pre-processing. During image denoising process, the key issue is how to suppress the noise while pre-serving image detailed features as much as possible(such as edge, texture, etc.).Wavelet packet analysis and partial differential equation are the two more effi-cient image denoising methods and are developed in recent years.In this paper,we con-duct deep study and summary on wavelet packet analysis method and total variation method,in accordance with their respective denoising characteristics, propose a new denoising algorithm, which is denoising algorithm based on wavelet packet and total variation.In the second chapter,we describe the basic theory of the wavelet transform and wavelet packet transform and their applications in image denoising.In the third chapter,we describe the principle of denoising and introduce several classical image denoising models based on total variation method,and have done fur-ther analysis and research for them.If ROF Method is directly applied to the noisy image,it is easy to think noise as edge, making the ladder effect produced in the image flat areas,however, with the increase of iteration times, image will become blurred, and thus can not achieve a good denoising effect.2007 years, Tony F. Chan and Hao-Min Zhou,proposed TV wavelet thresholding denoising model based on wavelet and total variation method.Through the variational model to select and modify the wavelet co-efficients so that reconstructed image has fewer oscillations near edge while noise is smoothed.Although this method can to some extent reduce the oscillations, the noise has not been well suppressed.The reason may be that this method is not a more general approach, may gain a better denoising effect for a particular image.The fourth chapter is the focus of this research work. Mainly combining advan-tages of wavelet packet analysis with advantages of total variation method, we propose a new image denoising method, which is image denoising algorithm based on wavelet packet and total variation. And comparing this method and present some classical denoising methods through numerical experiments, the experimental results show this method is feasible and effective.In this paper, we exploit the advantages of wavelet packet, contain an initial noise filter.As wavelet packet well removes image noise in flat regions, thus avoiding the phenomenon noise is not well smoothed. And wavelet packet transform conducts a more elaborate division of image high frequency part,which makes certain detailed features can be protected in denoising processing.Thus we apply total variation method to the preliminary processed image, making image after denoising have a better visual effect.With the analysis of both wavelet packet transform and denoising models based on total variation, this paper denoising algorithm can be described as follows:STEP1:For noisy imageu0(x, y), we use wavelet packet method to conduct pre-liminary noise processing for it. Specific steps are as follows.(1) We decompose imageuo(x,y) for four-layer.(2) Select the appropriate information cost function Q, we select the best wavelet packet basis according to information cost function Q.(3) To process wavelet packet coefficients under selected the best wavelet packet basis by the thresholding.(4) we use processed wavelet packet coefficients to reconstruct image.STEP2:Suppose new image after the initial treatment for u1(x, y), we use u1(x, y) to replace uo(x,y) of the following equation,and acquire final solution by solving the equation.In numerical experiments, we compare this method with ROF method, soft thresh-olding denoising method and TV wavelet thresholding denoising method. Experimen-tal results show this method both in visual effect and in the peak signal to noise ratio respect, can achieve better results.更多还原