压缩感知l1-αl2模型下的DCA算法分析
Analysis of the DCA Algorithm Under the l1-αl2 Model of Compressive Sensing
宋儒瑛 1吴丽君1
作者信息
- 1. 太原师范学院 数学与统计学院,山西 晋中 030600
- 折叠
摘要
在压缩感知领域,对于从少量测量中恢复稀疏向量这个基本的问题,更倾向于相关性尽可能小的测量.然而在现实中利用l1,l2 等传统方法的计算成本较高,因此文章在新模型l1-αl2(0<α≤1)下,利用‖x‖1-α‖x‖2 最小化来解决压缩感知问题,基于凸函数的差分算法,文中得到了求解l1-αl2 极小化问题的迭代算法,并进行了理论分析,证明了该算法收敛于一个满足最优性条件的稳定点.
Abstract
In the field of compressed sensing,we prefer measurements with as little correlation as possible for the basic problem of re-covering sparse vectors from a small number of measurements.However,in reality,the calculation cost of using such l1,l2 traditional methods is higher.Therefore,in this paper,under the new model l1-αl2(0<α≤1),we use minimization of ‖x‖1-α‖x‖2 to solve the compressed sensing problem.Difference algorithm based on convex function,an iterative algorithm for solving the l1-αl2 minimization problem is obtained in this paper,it is proved that the algorithm converges to a stable point which satisfies the optimality condition.
关键词
压缩感知/l1-αl2最小化/DCA算法Key words
compressed Sensing/l1-αl2 minimization/DCA(Difference of Convex functions Algorithm)引用本文复制引用
出版年
2024
NETL
NSTL
万方数据