实际图像在采集、获取以及传输的过程中，往往受到噪声的污染，成为降质图像。噪声极大地影响了图像的信息提取。为了后续更高层次的处理及应用，很有必要对图像进行去噪处理。有些图像数据量极为庞大，比如合成孔径雷达(SAR-Synthetic Aperture Radar)图像。对于这些图像来说，好的去噪算法不仅要获得良好的去噪效果，还必须执行高效。本文对基于整数小波(IWT-Integer Wavelet Transform)与GCV(Generalized Cross Validation)的图像去噪算法进行了深入研究，在GCV的基础上提出了FGCV(fast GCV)，提高了寻找阈值的速度。最后将IWT与FGCV应用到SAR图像的去噪中。近些年来，小波阈值去噪算法在图像处理领域中取得了非常可观的成果。传统小波去噪在一定程度上抑制噪声的同时，能够很好地保留边缘信息，且使得无伪边缘产生，但其存在着缺点：离散小波变换后的图像系数均为浮点数，使得图像有损；变换过程需要引入大量的卷积操作，使得计算复杂度偏高，对于数据量非常大的图像，计算量极为庞大；为了保证变换的完整性，必须在小波变换前对图像做边界延拓，增加编解码的复杂度与相应的存储开支。而基于提升框架的IWT在继承传统小波优点的同时，也弥补了其不足。本论文研究了多种整数小波变换，选取其中执行效率最高的5/3小波用于图像的小波去噪。小波阈值去噪算法中一个关键问题是选择合适的阈值。所谓最优阈值，就是使得去噪后图像与真实数据差值最小的阈值。在众多的小波阈值去噪算法中，多数是利用噪声的统计特性来计算最优阈值的。但在很多实际应用中，有关噪声的先验知识却是未知的，需要对其进行估计。而利用GCV函数来确定阈值，它只依赖于输入和输出数据，而和噪声能量及其真实数据无关，而且，Maarten Jansen等人已经证明：利用GCV所求得的阈值是一种最小均方误差意义上的渐进最优解。因此，利用GCV原理来求阈值，无需预先获取噪声的任何信息，而且在去噪的同时也能较好地保持原图像的细节特性。虽然GCV的计算速率很快，但是对于SAR图像而言，计算量还是相当可观的。为了提高阈值求取函数的执行速率，本文通过对GCV求解过程进行化简，并加大执行步长，提出了FGCV。FGCV与GCV相比，所求的最佳阈值一致，但是执行速率有了明显提高。论文将基于5/3整数小波与FGCV的去噪算法用于普通图像及SAR图像去噪。作者在VC++6.0环境下开发了两个处理平台：一般数字图像去噪平台与SAR图像去噪平台。用多幅图像进行了仿真实验，结果证实本文提出的算法去噪效果良好，并且效率较高。求解阈值过程中，FGCV所耗时间比GCV耗时缩减了50%以上。总而言之，本文提出的基于IWT与FGCV结合的图像去噪算法，不仅在一定程度上抑制了噪声，效率也有显著提升。

The image is often corrupted by noise in its collection, acquisition or transmission. Because the noise is the main factor that influenced image quality and greatly affected to extract the information from it, it must be removed before it can be analyzed and utilized. Some images such as synthetic aperture radar (SAR) images consist of a great mount of data. So an excellent image de-noising algorithm must have both good performance and good efficiency.In this paper an image de-noising algorithm, which is based on Integer-to-integer Wavelet Transform (IWT) and Fast Generalized Cross Validation (FGCV), is presented and applied to SAR images.In the last several years, wavelet thresholding has shown remarkable results in digital image de-noising. A classical wavelet transform maps floating point numbers to floating point numbers. However, most images consist of integer values only. IWT, which is based on the so called lifting scheme, is an alternative and faster algorithm for a classical wavelet transform. In this paper digital images and SAR images are de-noised with 5/3 IWT, which is more efficient than other IWT algorithms.The main issue in de-noising algorithms based on wavelet thresholding is the selection of the threshold. The optimal threshold minimizes the error of the result as compared to the unknown, exact data. This optimum cannot be found exactly, simply because the exact data are unknown. To estimate this optimal threshold, we use Generalized Cross Validation (GCV). Different from other threshold procedure, GCV allows choosing the (nearly) optimal threshold, without estimate for the noise energy. Though computation of GCV is quick, for large images time may become crucial. To speed up the computations of GCV, this paper presents FGCV, which is based on GCV but simplifies the procedure of GCV. FGCV has the same solution as GCV, and is more efficient than GCV. The image de-noising algorithm based on IWT and FGCV is applied to digital images and SAR images. It’s proved that the algorithm proposed in this paper de-noises images effective and efficient. Compared to GCV, the computations of FGCV spend less than half of the time.In one word, the de-noising algorithm presented in this paper does not only have good performance, but also be efficient.