摘要压缩感知理论是基于信号的稀疏性或可压缩性，在信号采样的同时进行压缩，可通过远低于奈奎斯特采样率的采样数据准确重建原始信号，真正实现了直接高效的“信息获取”。压缩感知理论主要包括三部分内容：稀疏表示、线性随机采样和非线性重建。其中，非线性重建是压缩感知理论的关键步骤和主要内容，重建算法的优劣直接影响着信号的重建精度和质量。相对于线性的非自适应采样过程，压缩感知重建是非线性且自适应的。论文以一维信号对压缩感知重建算法中的几种算法进行实现并比较，得出以下结论：

(1)在相同重建条件下凸优化算法的重建精度较高。67661

(2)贪婪算法在处理大规模信号时，体现出其良好的时间复杂度，能够在较短的时间内完成信号的重建。

毕业论文关键词   压缩感知  稀疏性  非线性重建

毕业设计说明书（论文）外文摘要

Title         Realization and comparison of   compressed sensing reconstruction algorithms       

Abstract

The theory of compressed sensing (CS) relies on the fact that most of the natural signals can be sparsely represented in some transform domain. CS is an approach to simultaneous sensing and compression which can acquire the signal from far fewer samples or measurements than the traditional methods use, and CS tell us that the incomplete measurement values can preserve the necessary information of the sparse and compressible signals. There are three import ant components in the CS theory, the first is the sparse representation of signal, the second is the linear measurement,and the last one is the nonlinear reconstruction. Among the three components, the nonlinear reconstruction is the key step for the whole CS acquisition process.This paper focuses on the reconstruction algorithms for the image.The main innovative results are listed as follows.

(1) With the same conditions, the convex optimization algorithms have higher precision then the greedy ones.

(2) The greedy algorithms in dealing with large signals, are good in time complexity, and can complete the signal reconstruction in a relatively short period of time.

Keywords  Compressed Sensing  Sparseness  Nonlinear              Reconstruction

目   次

1  绪论 5

1.1  研究背景及意义 5

1.2  压缩感知理论基础 6

1.2.1  稀疏表示 6

1.2.2  线性压缩测量 6

1.2.3  压缩感知非线性重建 7

1.3  本文的主要研究工作 8

2  算法介绍 8

2.1  贪婪算法 8

2.1.1  OMP算法 8

2.1.2  CoSaMP算法 9

2.2  凸优化算法 10

2.2.1  FISTA算法 10

2.2.2  PALM算法 11

2.2.3  DALM算法 12

3  实验结果及分析 13

3.1  凸优化算法比较分析 13

3.2  贪婪算法比较分析 15

3.3  类别比较