压缩感知理论是信号采集和处理的一门新理论, 它突破了传统的nyquist-shannon(奈奎斯特-香农)采样定理对采样频率的要求, 可以利用远小于采样定理要求的采样次数来重构原始信号[1]。首先介绍了三种常用的随机矩阵的构造方法, 随后介绍了不同类型的压缩感知算法, 并对其中两种算法进行了仿真与比较, 在此基础上仿真了不同测量矩阵下不同噪声水平下算法对图像重构质量的影响, 经过仿真分析TVAL3算法在图像重构时间和噪声抑制方面表现突出。

Compressive sensing reconstruction is a new theory of signal acquisition and processing, which breaks through the traditional sampling theorem’s requirements on Nyquist sampling frequency and the original signal can be reconstructed for sampling times far less than the requirements of sampling theorem. At first, three methods of constructing random matrix are introduced. And then, different kinds of compressive sensing algorithms are introduced, and two of them are simulated and compared. At last, based on this, the influence of the algorithm on image reconstruction quality under different noise levels of measurement matrix is simulated. Through simulation analysis, total variation augmented lagrangian 3 (TVAL3) algorithm is outstanding in image reconstruction time and noise reduction.