【作者】 欧阳宏斌；

【导师】 韦志辉；

【作者基本信息】 南京理工大学 ， 应用数学， 2004， 硕士

【摘要】 小波变换作为一种新的多分辨分析方法，因其具有时频局部化和变分辨特性而特别适合处理非平稳信号。由于小波域阈值方法的缺点是在图像灰度值发生跳变的地方会出现振荡现象，并随着噪声污染程度的增高而更加明显。为了克服振荡现象，针对小波收缩方法中产生明显的“Gibbs”现象，将著名的总体变差模型嵌入小波收缩的框架，不仅能消除“Gibbs”现象，还能使小波收缩框架下TV滤波简单易行。该模型中利用改进小波阈值技术选取合适的需要保留的小波系数，然后对该系数重建图像进行空域各向异性扩散处理。本文提出了该变分问题完整的空域和小波域交替迭代的图像恢复算法。实验证明该算法不仅能够很好地抑制噪声和保持边缘，而且重构的图像能够减少边缘的振动，是一种行之有效的提高图像视觉品质的算法。更多还原

【Abstract】 It is widely accepted that the wavelet transform (DWT) is a very attractive tool to deal with non-stationary signal due to the muti-resolution property. However, Gibbs phenomena and artifacts may be caused near the edges if the wavelet coefficients are modified by wavelet visual shrinking threshold. To overcome this problem, the wavelet based total variation regularized model is established according to the image restoration model of L.Rudin, S.Osher and E.Fatemi. In this method, wavelet coefficients to be filtered are selected by wavelet threshold technique. Then the image reconstructed by the nonzero wavelet coefficients is selective smoothing. We propose a complete numerical iterative scheme for this variational problem. Experiments show our algorithm is efficiency to improve the image’s visual quality, and achieve a better compromise between noise suppressing and edge preserved, furthermore the reconstructing image has less oscillations near edges.更多还原