中文摘要：

随着信息技术的不断发展，人们对信息需求量越来越大，这给信号采样、传输和存储的实现带来的压力越来越大。近年来国际上出现的压缩传感理论为该问题的解决提供了新的解决方案。压缩传感理论首先将信号投影到一个低维的信号空间，然后通过解一个基于凸优化的非线性恢复算法将信号恢复，而仅仅需要很少的数据。介绍了CS理论框架并对其中存在的难点问题进行了探讨，主要有稀疏近似理论、观测矩阵、信号重建算法。最后将压缩传感理论应用到一维和二维图像数据重建中并给出了仿真结果。实验结果表明，该方法与传统压缩方法相比具有更高的压缩比，并且能够得到更小的压缩误差。

英文摘要：

With the development of information technology, the demands for information are incressing dramatically, which causes a series of challenges in signal sampling, transmission and storage. An emerging theory of compressed sensing （CS） ,which is presented in recent years, provides a new method for solving this problem. CS project a singnal into a lower dimension at frist , then by using nonlinear recovery algorithms （based on convex optimization）, super- resolved signals and images can be reconstructed from what appears to be highly incomplete data. Introduces the processing of the signal sparse representation, observation matrix and recovery algorithms and focus on the theoretical framework of oompressed sensing and discusses the existing difficult problems. Apply this new theory to data of one dimension and image of two dimensions and give the simulated result in the end. Experiments proved CS is higher compression ratio and smaller compression error than traditional data compression algorithm.