| 基于部分支撑集的L1范数稀疏重构算法 |
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| 引用本文： | 付卫红,梁漠杨,田德艳,农斌.基于部分支撑集的L1范数稀疏重构算法[J].计算机仿真,2020,37(2):174-177,311. |
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| 作者姓名： | 付卫红 梁漠杨 田德艳 农斌 |
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| 作者单位： | 西安电子科技大学通信工程学院,陕西西安710071;西安中电科西电科大雷达技术协同创新研究院有限公司,陕西西安710071;西安电子科技大学通信工程学院,陕西西安710071 |
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| 基金项目： | 国家自然科学基金;高等学校学科创新引智计划计划) |
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| 摘 要： | 针对压缩感知理论中,现有的优化L1范数稀疏重构算法在重构源信号时,当且仅当稀疏度小于等于观测信号长度一半时才能够正确重构源信号的问题,提出了部分支撑集的L1范数稀疏重构算法。改进算法采用线性规划方法最小化源信号"尾部"支撑集的L1范数,能够在稀疏度大于观测信号长度一半时正确重构出源信号。仿真结果表明,在不同信噪比和稀疏度条件下,所提算法的重构精度优于现有的优化L1范数的稀疏重构算法和正交匹配追踪的稀疏重构算法。
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| 关 键 词： | 压缩感知 部分支撑集 稀疏重构 线性规划 |
Algorithm for Sparse Recovery Based on the L1 Norm Of Partial Support Set |
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| FU Wei-hong,LIANG Mo-yang,TIAN De-yan,NONG Bin.Algorithm for Sparse Recovery Based on the L1 Norm Of Partial Support Set[J].Computer Simulation,2020,37(2):174-177,311. |
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| Authors: | FU Wei-hong LIANG Mo-yang TIAN De-yan NONG Bin |
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| Affiliation: | (School of Telecommunication Engineering,Xidian University,Xi'an Shanxi 710071,China;Collaborative Innovation Center of Information Sensing and Understanding,Xi'an Shanxi 710071,China) |
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| Abstract: | Aiming at the problem that the sparsity of the existing optimizing L1 norm sparse recovery algorithm can not recover the source signal until the sparsity is less than or equal to half of the measurement's length in compressed sensing,an algorithm for sparse recovery of the L1 norm of partial support set is proposed in the paper.The improved algorithm can minimize the L1 norm of the"tail"support set of the source signal by using the linear programming method,recovering the source signal even if the sparsity is larger than half of the measurement's length.The simulation results indicate that the reconstruction accuracy of the proposed algorithm is better than the existing sparse recovery algorithms of optimizing L1 norm and OMP under different SNR and sparsity conditions. |
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| Keywords: | Compressed sensing Partial support set Sparse recovery Linear programming |
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