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基于迭代加权l1正则化的分布式联合稀疏优化
引用本文:吴迪,葛临东,彭华.基于迭代加权l1正则化的分布式联合稀疏优化[J].信息工程大学学报,2014(3):299-305.
作者姓名:吴迪  葛临东  彭华
作者单位:信息工程大学,河南郑州450001
基金项目:国家自然科学基金资助项目(61072046);河南省基础与前沿计划(102300410008,132300410049)
摘    要:多测量向量模型中的联合稀疏信号重构是压缩感知理论中的重要研究内容。针对分布式网络中的联合稀疏优化问题,给出了一种基于迭代加权l1正则化的分布式联合稀疏优化算法。该算法采用迭代加权l1正则化算法提高稀疏信号的重构质量,然后将与联合支撑相关的加权向量作为一致性约束,采用交替方向乘子法求解一致优化问题来更新加权向量。该分布式联合稀疏优化算法通过每个节点的稀疏优化以及单跳邻居节点间的信息交换达到集中式优化的性能,避免了数据集中带来的网络通信负担。仿真结果表明,给出的分布式联合稀疏优化算法具有良好的重构性能和较快的收敛速度。

关 键 词:联合稀疏优化  迭代加权  分布式算法  一致优化  多测量向量

Distributed Jointly Sparse Optimization Based on Iteratively Reweighted l1 Regularization
WU Di,GE Lin-dong,PENG Hua.Distributed Jointly Sparse Optimization Based on Iteratively Reweighted l1 Regularization[J].Journal of Information Engineering University,2014(3):299-305.
Authors:WU Di  GE Lin-dong  PENG Hua
Affiliation:(Information Engineering University, Zhengzhou 450001, China)
Abstract:Reconstructing jointly sparse signals from multiple measurement vectors is an important research content in compressive sensing. In distributed networks, a distributed jointly sparse optimization algorithm based on iteratively reweighted l1 regularization is proposed. It adopts iteratively reweighted l1 regularization algorithm to improve the reconstruction quality. Then the consensus constraints are imposed on one-hop neighbors such that neighboring local copies of weight vector associated with the joint support are equal. The alternating direction method of multipliers is also used to solve the consensus optimization problem iteratively to update the weight vector. The proposed algorithm performs the task based on the local computations at each agent and the information is exchanged with its neighbors, which can reach the performance of centralized solution but reduce the burden of network communication. Simulation results show that the algorithm has good reconstruction performance and fast convergence rate.
Keywords:jointly sparse optimization  iteratively reweighted  distributed algorithm  consensus op-timization  multiple measurement vectors
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