压缩感知问题的目标罚函数交替随机搜索方法

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英文篇名：Alternate Random Search Algorithm of Objective Penalty Function for Compressed Sensing Problem 作者：蒋敏 ; 孟志青 ; 沈瑞 英文作者：JIANG Min;MENG Zhi-qing;SHEN Rui;School of Management,Zhejiang University of Technology;School of Economics,Zhejiang University of Technology; 关键词：压缩感知 ; 等价表示 ; 稀疏优化 ; 目标罚函数 ; 交替随机搜索算法 英文关键词：Compressive sensing;;Equivalent representation;;Sparse optimization;;Object penalty function;;Alternating random search algorithm 中文刊名：JSJA 英文刊名：Computer Science 机构：浙江工业大学管理学院;浙江工业大学经济学院; 出版日期：2019-06-15 出版单位：计算机科学 年：2019 期：v.46 基金：浙江省自然科学基金项目(LY18A010031);; 国家自然科学基金项目(11871434)资助 语种：中文; 页：JSJA2019S1027 页数：5 CN：S1 ISSN：50-1075/TP 分类号：143-147

摘要

首先将压缩感知优化问题等价定义为双凸优化问题,证明了这个等价双凸优化问题的最优解也是压缩感知优化问题的最优解,然后定义了它的一个具有2阶以上的光滑性的目标罚函数及对应的交替子问题,给出了一个交替求解子问题迭代算法,理论上证明了所提出的交替算法的收敛性定理,导出了压缩感知的最优解显示表达式,设计了一种对一类特定的压缩感知问题有效的交替随机搜索算法。该方法为研究和解决实际的压缩感知问题提供了一种新的设计思路。
        The compressed sensing optimization problem was defined as a biconvex optimization problem.It is proved that the optimal solution of the equivalent biconvex optimization problem is also the optimal solution of the compressed sensing optimization problem.Then a smooth objective penalty function and its corresponding alternating sub-problem were defined.An iterative algorithm for solving the sub-problem was given.The convergence theorem of alternating algorithm was proved theoretically.The expression of the optimal solution for compression perception was derived.An alternating random search algorithm was designed,which is effective for a specific type of compressed sensing problem.This method provides a new design idea for studying and solving the actual compressed sensing problem.

引文

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