代冀阳, 李兴坤, 吴国辉. 一种叠加矩阵在信号重构中的应用研究[J]. 南昌航空大学学报(自然科学版), 2014, 28(4): 6-12. DOI: 10.3969/j.issn.1001-4926.2014.04.002
引用本文: 代冀阳, 李兴坤, 吴国辉. 一种叠加矩阵在信号重构中的应用研究[J]. 南昌航空大学学报(自然科学版), 2014, 28(4): 6-12. DOI: 10.3969/j.issn.1001-4926.2014.04.002
DAI Ji-yang, LI Xing-kun, WU Guo-hui. Application and Study of A Superimposed Measurement Matrix in Signal Reconstruction[J]. Journal of nanchang hangkong university(Natural science edition), 2014, 28(4): 6-12. DOI: 10.3969/j.issn.1001-4926.2014.04.002
Citation: DAI Ji-yang, LI Xing-kun, WU Guo-hui. Application and Study of A Superimposed Measurement Matrix in Signal Reconstruction[J]. Journal of nanchang hangkong university(Natural science edition), 2014, 28(4): 6-12. DOI: 10.3969/j.issn.1001-4926.2014.04.002

一种叠加矩阵在信号重构中的应用研究

Application and Study of A Superimposed Measurement Matrix in Signal Reconstruction

  • 摘要: 为提高压缩感知算法的信号重构质量,基于傅里叶随机测量矩阵的构造方法,提出一种叠加测量矩阵。该矩阵通过在傅里叶随机矩阵的基础上叠加确定性类圆环矩阵,重新调整测量结构和范围,使信号在压缩传感过程中能完整、准确地保留有用信息。在分析几类常用测量矩阵的基础上,着重介绍了该叠加测量矩阵的构造方法,并应用于一、二维信号重构中。通过对这几类测量矩阵的重构效果进行仿真比较,结果显示,在相同的信号稀疏度、测量比例和重构算法情况下,改进的测量矩阵能极大提高信号重构的质量。

     

    Abstract: In order to improve the quality of the signal which using compressed sensing algorithm for reconstruction, based on the construction method of fourier random measurement matrix, this paper presents a superimposed matrix. The matrix superposed deterministic ring matrix on the basis of fourier random matrix, readjust measurement structure and range, so that the signal retain the useful information completely and accurately in the process of compressed sensing. This paper focuses on the construction methods of the superimposed measurement matrix by analysis types of common measurement matrix, which applied to 1D and 2D signals reconstruction. Through the simulation comparison of the reconstruction effects of these matrixes, we find that the improved measurement matrix can improve the quality of the signal reconstructed in the same signal sparsity, measuring proportion and reconstruction algorithm.

     

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