易于硬件实现的压缩感知观测矩阵的研究与构造

Study and construction of a compressed sensing measurement matrix that is easy to implement in hardware

在压缩感知过程中,观测矩阵在信号采样及重构中具有重要作用,构造易于硬件实现、结构简单且占内存较小的观测矩阵是压缩感知理论能否实际应用的关键问题之一。提出两种易于硬件实现的观测矩阵,即顺序部分哈达玛观测矩阵和循环伪随机观测矩阵,其中循环伪随机观测矩阵可分为循环m序列和循环gold序列,并证明了伪随机序列所构造的观测矩阵满足有限等距准则。为验证上述两种观测矩阵性能,对二维图像信号进行仿真,结果表明,在较低的采样率下顺序部分哈达玛观测矩阵的重构效果最优,但是采样信号长度必须是2的k次幂;循环伪随机观测矩阵的重构效果虽然弱于顺序部分哈达玛观测矩阵,但是明显优于高斯随机观测矩阵,克服了顺序部分哈达玛矩阵观测信号必须是2的k次幂的限制。提出的两种观测矩阵易于硬件实现,避免了随机矩阵的不确定性且克服了随机矩阵浪费存储资源的缺陷,具有良好的实际应用价值。

In the compressed sensing process,the measurement matrix plays a significant role in signal sampling and reconstruction. Therefore,a measurement matrix that is simple in structure,has a small memory,and is easy to implement in hardware is the key to applying compressed sensing theory. Based on the partial Hadamard measurement matrix and a circulating pseudo-random sequence,this paper presents two measurement matrixes that are easy to implement in hardware,namely the sequence partial Hadamard measurement matrix and the recycled pseudo-random sequence measurement matrix. The latter consists of a recycled m sequence and a recycled gold sequence measurement matrix. This further proves that a measurement matrix constructed by a pseudo-random sequence complies with the RIP principle. To test the performance of the two measurement matrixes,a twodimensional image signal was simulated. It was found that under a low sampling rate,the reconstruction of the sequence partial Hadamard measurement matrix is optimal provided that the length of the sampling signal is 2k.Although reconstruction of the recycled pseudo-random sequence measurement matrix is inferior to the sequence partial Hadamard measurement matrix,it exceeds the Gaussian random measurement matrix,and also overcomes the sequence partial Hadamard measurement matrix 's limitation of a 2ksignal length. These two types of measurement matrix are easy to implement in hardware,and avoid the uncertainty and storage waste of a random matrix. Therefore,they are suitable for practical application.