Measurement matrix construction algorithm for sparse signal recovery
Measurement matrix construction algorithm for sparse signal recovery
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DOI：
10.1109/i2mtc.2013.6555575
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发表时间：
2013-05
期刊：
影响因子：
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通讯作者：
Wenjie Yan;Qiang Wang;Yi Shen;Zhenghua Wu
中科院分区：
文献类型：
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作者：
Wenjie Yan;Qiang Wang;Yi Shen;Zhenghua Wu
提出了一种基于压缩感知的简单测量矩阵构造算法。在压缩感知中，测量矩阵和稀疏字典（基）之间的较小相干性可以具有更好的信号重构性能。随机测量矩阵（例如，高斯矩阵）已被广泛使用，因为它们与几乎任何稀疏基呈现小相干性。然而，通过降低与固定稀疏基的相干性来优化测量矩阵将大大改善CS性能，这一结论已被许多研究人员所证明。在此基础上，我们采用了收缩和奇异值分解（SVD）技术来实现这一目的。最后，优化后的矩阵和稀疏字典列间的一致性大大降低，甚至接近于Welch界。此外，我们建立了几个实验来测试所提出的算法的性能，并与最先进的算法进行比较。我们得出结论，贪婪算法的恢复性能（例如，正交匹配追踪）的性能优于传统的随机矩阵算法、Elad算法、Vahid算法和Xu提出的优化矩阵算法。
A simple measurement matrix construction algorithm (MMCA) within compressive sensing framework is introduced. In compressive sensing, the smaller coherence between the measurement matrix and the sparse dictionary (basis) can have better signal reconstruction performance. Random measurement matrices (e.g., Gaussian matrix) have been widely used because they present small coherence with almost any sparse base. However, optimizing the measurement matrix by decreasing the coherence with the fixed sparse base will improve the CS performance greatly, and the conclusion has been well proved by many prior researchers. Based on above analysis, we achieve this purpose by adopting shrinking and Singular Value Decomposition (SVD) technique iteratively. Finally, the coherence among the columns of the optimized matrix and the sparse dictionary can be decreased greatly, even close to the welch bound. In addition, we established several experiments to test the performance of the proposed algorithm and compare with the state of art algorithms. We conclude that the recovery performance of greedy algorithms (e.g., orthogonal matching pursuit) by using the proposed measurement matrix construction method outperforms the traditional random matrix algorithm, Elad's algorithm, Vahid's algorithm and optimized matrix algorithm introduced by Xu.