易于硬件实现的压缩感知观测矩阵的研究与构造

发布时间：2018-02-01 01:00

本文关键词： 图像处理机器视觉压缩感知采样及重构观测矩阵顺序部分哈达玛循环伪随机矩阵有限等距　出处：《智能系统学报》2017年03期 　论文类型：期刊论文

【摘要】：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。
[Abstract]:In the process of compression sensing, observation matrix plays an important role in signal sampling and reconstruction. The observation matrix with simple structure and small memory is one of the key problems whether the compressed sensing theory can be applied in practice. Two kinds of observation matrices which are easy to be realized by hardware are proposed. The order part of Hadamard observation matrix and cyclic pseudorandom observation matrix, in which cyclic pseudorandom observation matrix can be divided into cyclic m sequence and cyclic gold sequence. It is proved that the observation matrix constructed by pseudorandom sequence satisfies the finite equidistant criterion. In order to verify the performance of the two kinds of observation matrices, the two-dimensional image signals are simulated and the results show that. At low sampling rate, the reconstruction effect of sequential partial Hadamard observation matrix is optimal, but the sampling signal length must be k power of 2; Although the reconstruction effect of cyclic pseudo-random observation matrix is weaker than that of sequential partial Hadamard observation matrix, it is obviously superior to Gao Si random observation matrix. It overcomes the limitation that the observed signal of order part Hadamard matrix must be k power of 2. The two kinds of observation matrix are easy to be realized by hardware. It avoids the uncertainty of random matrix and overcomes the defect of wasting storage resource of random matrix, so it has good practical application value.
【作者单位】：中央民族大学信息工程学院;
【基金】：国家自然科学基金项目(51375504,61602539)
【分类号】：TN911.73
【正文快照】： Study and construction of a compressed sensing measurementmatrix that is easy to implement in hardwareLI Xiali,WU Licheng,FAN Yanming(School of Information Engineering,Minzu University of China,Beijing 100081,China)压缩感知(compressed sensing,CS)[1-3]通

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