摘要图像在获取、存储、传输等过程中都会受到特定噪声的污染，造成图像质量的下降，因此图像的重建是图像处理中的一个重要问题。其目的是通过一系列的运算，尽可能恢复原始图像。
近年来，稀疏表示理论受到人们的广泛关注。其理论依据是，具有一定光滑性的干净图像在适当的过完备字典下存在稀疏表示，通过选择或设计适当的字典，求出图像在该字典下的稀疏表示，就可以达到重建的目的。
图像的重建是图像处理的重要课题之一，即是试图利用退化现象的某种先验知识来重建或恢复被退化的图像，最终达到改善给定图像的目的。图像复原技术经过几十年的发展，逐步形成了一套统一的理论框架。
本毕业论文研究了在两种不同字典下的稀疏表示，同时实现基于稀疏正则化的图像信号复原。实验结果表明，曲波字典比小波字典具有更好的适应性。
关键词  数字图像处理  稀疏表示   正则化  图像重建7090
毕业设计说明书（论文）外文摘要
Title   Image reconstruction  algorithm  based on the sparse representation
Abstract
Images in the process of acquisition, storage, and transmission are subject to specific noise pollution, which can cause the decline in image quality. So, the image denoising reconstruction is an important issue in image processing. Its goal is to restore the original image as far as possible by a series of operations .In recent years, the sparse representation theory has been widespread concerned. Its theoretical basis is that a clean image with a certain smoothness exists sparse in an appropriate complete sub Highness or designing appropriate dictionary.  We can get the purpose of denoising by finding the image in the dictionary under the sparse  selecting .Reconstruction of the image is one of the important topics of image processing, that is trying to use some a priori knowledge to rebuild or restore the degraded image , and ultimately reach the purpose to improve the given image. After decades of development, image restoration techniques are gradually formed a unified theoretical framework .This paper based on the sparse representation of two different dictionaries, and at the same time to achieve recovery based on the sparse regularization of the image signal. Experimental dismissal the curvelet dictionary has better adaptability than the wavelet  dictionary.
Keywords  Digital image processing  sparse  regularization  image reconstruction
      目   次  
1  引言    1
1.1  课题的背景    1
1.2  数字图像处理的概念    1
1.3  小波理论与曲波理论    2
1.4  文章的组织    2
2  信号表示理论    3
2.1  基    3
2.2  框架    3
2.3  字典    4
2.4  信号的稀疏表示    4
2.5  压缩感知    8
3  小波与曲波    9
3.1  小波分析    9
3.2  曲波分析    14
3.3  总结    17
4  图像信号复原方法    17
4.1  信号去噪    18
4.2  信号反卷积    19
4.3  信号超分辨率重建    19
4.4  信号分离    19
4.5  凸优化算法    20
5  实验研究    22
5.1  基于小波字典的稀疏重建    22
5.2  基于曲波字典的稀疏重建    22
5.3  研究结果    23 基于稀疏表示的图像重建算法研究+文献综述:http://www.youerw.com/tongxin/lunwen_4860.html