| A-线性Bregman 迭代算法 |
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| 引用本文： | 张慧,成礼智.A-线性Bregman 迭代算法[J].计算数学,2010,32(1):97-104. |
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| 作者姓名： | 张慧 成礼智 |
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| 作者单位： | 国防科技大学理学院数学系,长沙,410073 |
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| 基金项目： | 国家自然科学基金,全国优秀博士论文基金 |
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| 摘 要： | 线性Bregman迭代是Osher和Cai等人最近提出的一种在压缩感知等领域有重要作用的有效算法.本文在矩阵A非满秩情形下,研究了求解下面最优化问题的线性Bregman迭代:min u∈R~M{‖u‖_1:Au+g}给出了一个关于线性Bregman迭代收敛性定理的简化证明,设计了一类A~-线性Bregman迭代算法,并针对A~+情形证明了算法的收敛性.最后,用数值仿真实验验证了本文算法的可行性.
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| 关 键 词： | 基追踪 线性Bregman迭代 压缩感知 最优化 |
| 收稿时间： | 2009-01-13 |
A- LINEARIZED BREGMAN ITERATION ALGORITHM |
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| Zhang Hui,Cheng Lizhi.A- LINEARIZED BREGMAN ITERATION ALGORITHM[J].Mathematica Numerica Sinica,2010,32(1):97-104. |
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| Authors: | Zhang Hui Cheng Lizhi |
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| Institution: | College of Science,National University of Defense and Technology, Changsha 410073, China |
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| Abstract: | Linearized Bregman iteration is an efficient algorithm in many areas such as compressed sensing which was proposed by Osher and Cai,et al,recently. In this paper, this iteration for the following minimization problem is studied as the matrix A is not surjective:
A simplify proof of the convergence of the linear Bregman iteration is given. A novel A- linear Bregman iteration is proposed and its convergence is proved for special case. Numerical results demonstrate that this novel iteration can recovery sparse signal from linear measurements.
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| Keywords: | basis pursuit linearized Bregman iteration compressed sensing optimiza-tion |
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