Xu Qiangrong, Sheng Zhichao, Fang Yong, Zhang Liming
Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai 200444, China.
Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Macau 999078, China.
Sensors (Basel). 2021 Feb 9;21(4):1229. doi: 10.3390/s21041229.
Compressed sensing (CS) has been proposed to improve the efficiency of signal processing by simultaneously sampling and compressing the signal of interest under the assumption that the signal is sparse in a certain domain. This paper aims to improve the CS system performance by constructing a novel sparsifying dictionary and optimizing the measurement matrix. Owing to the adaptability and robustness of the Takenaka-Malmquist (TM) functions in system identification, the use of it as the basis function of a sparsifying dictionary makes the represented signal exhibit a sparser structure than the existing sparsifying dictionaries. To reduce the mutual coherence between the dictionary and the measurement matrix, an equiangular tight frame (ETF) based iterative minimization algorithm is proposed. In our approach, we modify the singular values without changing the properties of the corresponding Gram matrix of the sensing matrix to enhance the independence between the column vectors of the Gram matrix. Simulation results demonstrate the promising performance of the proposed algorithm as well as the superiority of the CS system, designed with the constructed sparsifying dictionary and the optimized measurement matrix, over existing ones in terms of signal recovery accuracy.
压缩感知（CS）已被提出，用于在感兴趣的信号在某个域中稀疏的假设下，通过同时对信号进行采样和压缩来提高信号处理效率。本文旨在通过构建一种新型的稀疏化字典并优化测量矩阵来提高CS系统性能。由于竹中 - 马尔姆奎斯特（TM）函数在系统识别中的适应性和鲁棒性，将其用作稀疏化字典的基函数会使所表示的信号比现有的稀疏化字典呈现出更稀疏的结构。为了降低字典与测量矩阵之间的互相关性，提出了一种基于等角紧框架（ETF）的迭代最小化算法。在我们的方法中，我们在不改变传感矩阵相应Gram矩阵性质的情况下修改奇异值，以增强Gram矩阵列向量之间的独立性。仿真结果证明了所提算法的良好性能，以及使用所构建的稀疏化字典和优化的测量矩阵设计的CS系统在信号恢复精度方面优于现有系统。
