压缩感知中l1问题的自适应罚参数交替方向法

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徐丽君,胡瑞戈,李婷.压缩感知中l1问题的自适应罚参数交替方向法[J].,2022,62(1):95-101

压缩感知中l1问题的自适应罚参数交替方向法

Alternative direction method with adaptive penalty parameter for l1 problem in compressed sensing

DOI：10.7511/dllgxb202201012

中文关键词:压缩感知基追踪问题自适应罚参数交替方向法对偶问题

英文关键词:compressed sensing basis pursuit problem adaptive penalty parameter alternative direction method dual problem

基金项目:中央高校基本科研业务费专项资金资助项目(3132021193)；中国博士后科学基金资助项目(2020M670717)；辽宁省教育科学“十三五”规划课题(JG20DB058).

作者	单位
徐丽君,胡瑞戈,李婷

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中文摘要:

为解决交替方向法中的罚参数选取问题，以压缩感知中l1问题为研究对象，提出了一种自适应罚参数调整准则．该准则基于交替方向法迭代过程中目标函数和约束条件的变化关系，通过详细研究调整罚参数的条件、频率和大小，给出了基于对偶问题交替方向法的罚参数动态调整方案．数值实验表明所提出的自适应罚参数调整准则使得初始罚参数的选取范围更大，提高了可适用性；并且在迭代过程中动态调整罚参数可以加快运行速度，大大提高了交替方向法效率．

英文摘要:

In order to deal with the choice of penalty parameter in the alternative direction method, an adaptively updating rule for penalty parameter is proposed specially for l1-problem in compressed sensing. The rule is based on the relative change of the objective value and constraints during iterations. By studying the condition, frequency and quantity of updating penalty parameter in detail, a dynamic scheme to adjust the penalty parameter is developed for the dual problem. Numerical experiments show that the proposed adaptively updating rule enlarges the choice of initial penalty parameter which improves the applicability. In addition, since the penalty parameter is dynamically adjusted during iterations, it can speed up the operation and achieve good performance for the alternative direction method.

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压缩感知中l1问题的自适应罚参数交替方向法

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