| 王月,覃亚丽.基于 SVD-Schmidt 正交化的压缩感知测量矩阵的优化[J].高技术通讯(中文),2024,34(10):1046~1057 |
| 基于 SVD-Schmidt 正交化的压缩感知测量矩阵的优化 |
| Optimization of compressed sensing measurement matrix based on SVD-Schmidt orthogonalization |
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| DOI：10. 3772 / j. issn. 1002-0470. 2024. 10. 004 |
| 中文关键词: 压缩感知(CS); 测量矩阵; 互相关性; 奇异值分解-施密特(SVD-Schmidt)正交化; 迭代优化 |
| 英文关键词: compressed sensing ( CS), measurement matrix, coherence, singular value decomposition-Schmidt (SVD-Schmidt) orthogonalization, iterative optimization |
| 基金项目: |
| 作者 | 单位 | | 王月 | (浙江工业大学信息工程学院 杭州 310023) | | 覃亚丽 | |
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| 摘要点击次数: 241 |
| 全文下载次数: 268 |
| 中文摘要: |
| 压缩感知(CS)理论中测量矩阵的性能优劣直接影响信号重构性能。 为了优化测量矩阵提高其重构性能,本文提出了一种基于奇异值分解-施密特( SVD-Schmidt)正交化的 CS 测量矩阵优化方法。 首先对测量矩阵进行奇异值分解(SVD)并选择最大的奇异值替换原来的奇异值形成新的矩阵,同时对其进行施密特正交化,对矩阵的列进行单位化,通过行和列不断循环交替自适应迭代优化得到优化后的测量矩阵。 通过一维信号和二维图像的仿真实验验证所提方法的优越性。 一方面,本文方法优化的测量矩阵互相关性明显降低;另一方面,实验仿真结果证明了测量矩阵经过优化之后提高了信号重构性能,本文方法重构性能优于现有的 SVD 法和特征值分解法。 |
| 英文摘要: |
| The performance of measurement matrices in compressed sensing (CS) theory affects the signal reconstruction
performance. In order to optimize the measurement matrix and improve its reconstruction performance, this paper
proposes an optimization method of CS measurement matrix based on singular value decomposition-Schmidt (SVD-
Schmidt) orthogonalization. Singular value decomposition(SVD) of the measurement matrix is performed and the
largest singular value is selected to replace original singular values to form a new matrix, and Schmidt normalization
of it is performed, columns of the matrix are unitized. The optimization measurement matrix is obtained by the
adaptive iterative optimization of rows and columns. The superiority of the proposed method is verified by simulation
experiments of one-dimensional signal and two-dimensional image. The proposed optimization measurement matrix
reduces the coherence obviously. Furthermore, the simulation results show that the signal reconstruction perform-
ance is improved after optimizing the measurement matrix, and the reconstruction performance of the proposed
method is better than that of the existing SVD method and eigenvalue decomposition method |
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