基于压缩感知的数据压缩理论及其重构算法对比研究

A theoretical introduction to compressive sensing theory and a comparative studies of reconstruction algorithm

压缩感知作为一种全新的信号采样理论，一经提出便引起广泛关注。本文拟在前人研究的基础上，通过理论研究及仿真实验对常见重构算法进行评价为后续理论研究及应用提供科学依据。首先对压缩感知的理论基础和主要构成进行阐述，以贪婪算法中的OMP算法分别对一维信号及不同类型的二维图像进行仿真实验，实验结果表明压缩感知算法可以在较低采样率下实现对一维或二维信号的高效重构，在采样率在0．5的情况下，其数据的压缩率达53％～60％。在系统总结几种常见重构算法特点的基础上，以标准测试影像为对象构建仿真实验，分别从重构算法的运算效率和重构质量两个方面对实验结果进行评价，结果显示IRLS算法重构精度较高，而GPSR算法的运算耗时较短。

The compressive sensing is a new theory, which attracted wide attentions from the world once it was proposed, In this study, we evaluated the advantages and disadvantages among various reconstruction algorithm through theoretical summary and simulation experiment, aiming at providing theoretical support for the research and application in the future, First of all, this thesis systematically summarized the theoretical framework and the main components of Compressive Sensing, and then carried out one-dimensional and two-dimensional simulation experiment by using OMP reconstruction algorithm, The result shows that the Compressive Sensing algorithm can reconstruct the original signal in a high probability even under a low sampling rate,In the case of the sampling rate is 0.5 ,the compressing rate was achieved to 53 %-60 %,Finally,in order to estimate the time spent during reconstructing and reconstruction precision of various reconstruction algorithm, we carried out another simulation experiment through standard test image based on the brief summary of the characteristics of these algorithms,The study shows that IRLS algorithm can provide a higher reconstruction accuracy, while the GPSR algorithm costs the minimum time to reconstruct the image.