| 基于随机间距稀疏 Toeplitz 测量矩阵的压缩传感 |
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| 引用本文： | 张成,杨海蓉,韦穗.基于随机间距稀疏 Toeplitz 测量矩阵的压缩传感[J].自动化学报,2012,38(8):1362-1369. |
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| 作者姓名： | 张成 杨海蓉 韦穗 |
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| 作者单位： | 1.安徽大学计算智能与信号处理教育部重点实验室 合 肥 230039; |
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| 基金项目： | 国家自然科学基金(60872106);安徽高校省级自然科学研究项目(KJ2011B131);安徽大学青年基金(KJQN1010);“新一代宽带无线移动通信网”国家科技重大专项(2009ZX-03006-001-02)资助~~ |
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| 摘 要： | 选择合适的测量矩阵是压缩传感理论实用化的关键之一. 本文在Toeplitz矩阵独立元素中随机地引入零元,形成随机间距稀疏Toeplitz矩阵, 使得随机独立变元个数可以减少到原Toeplitz矩阵的1/2～1/16,甚至更少, 非零元个数同样大大减少,有利于数据传输和存储.模拟实验表明随机间距稀疏 Toeplitz矩阵在重建效果优于Gauss矩阵和原Toeplitz矩阵的同时,重建时间只有Gauss矩阵和一般Toeplitz矩阵重建时间的约15%～40%.
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| 关 键 词： | 压缩传感 测量矩阵 托普利兹 确定性矩阵 |
| 收稿时间： | 2011-5-23 |
| 修稿时间： | 2011-8-12 |
Compressive Sensing Based on Deterministic Sparse Toeplitz Measurement Matrices with Random Pitch |
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| ZHANG Cheng,YANG Hai-Rong,WEI Sui.Compressive Sensing Based on Deterministic Sparse Toeplitz Measurement Matrices with Random Pitch[J].Acta Automatica Sinica,2012,38(8):1362-1369. |
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| Authors: | ZHANG Cheng YANG Hai-Rong WEI Sui |
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| Affiliation: | 1.Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230039;2.Department of Mathmatics, Hefei Normal University, Hefei 230609 |
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| Abstract: | Selecting an appropriate measurement matrix is one of the key points of compressive sensing. Due to randomly introducing zero elements into these matrices to form sparse Toeplitz matrices with random pitch, the number of random independent variables can be reduced to 1/2 and 1/16 less than that of original Toeplitz matrices, the number of non-zero elements can also be reduced significantly, which is conducive to data transmission and storage. Simulation results show that the reconstructions of sparse Toeplitz measurement matrices with random pitch are better than Gaussian and original Toeplitz matrices. Moreover, the time of reconstruction is only about 15% to 40% of the time of Gauss and general Toeplitz reconstruction. |
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| Keywords: | Compressive sensing measurement matrix Toeplitz deterministic matrix |
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