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Measurement Matrix Optimization for Compressed Sensing System with Constructed Dictionary via Takenaka–Malmquist Functions

机译：通过Takeaka-Malmquist函数用构造字典压缩传感系统的测量矩阵优化

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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.
机译：已经提出了通过同时采样并压缩信号在某个域中的信号稀疏的假设下进行感兴趣的信号来提高信号处理效率的效率。本文旨在通过构建新的稀疏字典和优化测量矩阵来改善CS系统性能。由于在系统识别中的Takea-Malmquist（TM）功能的适应性和稳健性，作为稀疏词典的基函数的使用使得所代表的信号表现出比现有的稀疏词典表现出稀疏结构。为了减少字典和测量矩阵之间的相互相干性，提出了基于等态的紧密帧（ETF）的迭代最小化算法。在我们的方法中，我们修改奇异值而不改变感测矩阵的相应克矩阵的特性，以增强克矩阵的列向量之间的独立性。仿真结果证明了所提出的算法的有希望的性能以及CS系统的优越性，在信号恢复精度方面，通过现有的稀疏字典和优化的测量矩阵设计。

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