中文摘要：

压缩感知是近年来,针对稀疏信号和可压缩信号的处理而出现的一种信号处理理论。测量矩阵是压缩感知理论中的一个至关重要的环节,它对信号采样和重构算法有着重要的影响。虽然一般传统的随机测量矩阵重建信号效果比较好,但有硬件实现比较困难的问题,并需要大量的存储空间和其他缺陷。确定性测量矩阵的出现,正好弥补了这些缺点。在本文中,基于信道编码中校验矩阵特性的优势,获得了满足有限紧致特性要求的确定性测量矩阵构造方法。把校验矩阵的列向量标准化、线性组合扩展到方阵、置换列向量后构成的矩阵作为确定性测量矩阵。这种方法可以在构造完成一个信道编码校验矩阵后,很容易构造对应的测量矩阵。数值结果表明,在相同重建算法和压缩比下,这种方法的性能和随机测量矩阵大致相若,甚至有所改善。同时,本文提出方法的构造时间较少,重建时只需要运行一次,可以满足实时性需求。为压缩感知算法的实际应用提供了一种有效的测量矩阵构造方法。

英文摘要：

Compressed sensing, which is the emergence of a signal processing theory sparse signal and compressible signals in recent years. The measurement matrix is a vital link in the compressed sensing theory, its signal sampling and reconstruction algorithm has an important impact. Although the traditional random measurement matrix for the re- construction is quite good, but its hardware implementation is difficult and requires a lot of storage space and other de- fects. While The emergence of the deterministic measurement matrix, makes up for these shortcomings. Using the ad- vantages of the channel coding check matrix, we put forward the way to meet the requirements of the restricted isometry property, through the constructor of the deterministic measurement matrix. We make the standardization of a parity check matrix of the column vector, and extend it to a square linear combination of the permutation matrix column vec-tor, then a deterministic measurement matrix can be created. This method ensure us to produce the measurement ma- trix easily, after we complete a channel encoded parity check matrix. Numerical results show that, under the same re-construction algorithm and compression ratio, the performance of this method is close to the random measurement ma-trix, even improved. The same time, it costs less time with the reconstruction being run once only, which can meet the real-time requirements. The practical application of the compressed sensing algorithm, provides an effective meas-urement matrix construction method.