压缩感知l_(1)-αl_(2)模型下的DCA算法分析  

Analysis of the DCA Algorithm Under the l_(1)-αl_(2)Model of Compressive Sensing

作　　者：宋儒瑛[1] 吴丽君 SONG Ruying;WU Lijun(School of Mathematics and Statistics,Taiyuan Normal University,Jinzhong 030600,China)

机构地区：[1]太原师范学院数学与统计学院,山西晋中030600

出　　处：《忻州师范学院学报》2024年第5期11-17,共7页Journal of Xinzhou Teachers University

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l,l_(2)等传统方法的计算成本较高,因此文章在新模型11-αl_(2)(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,l文中得到了求解l_(1)-αl_(2)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。In the field of compressed sensing,we prefer measurements with as little correlation as possible for the basic problem of recovering sparse vectors from a small number of measurements.However,in reality,the calculation cost of using such l_(1),l_(2) traditional methods is higher.Therefore,in this paper,under the new model l_(1)-αl_(2)(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 l_(1)-αl_(2) 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 l_(1)-αl_(2)最小化 DCA算法 

分 类 号：O211[理学—概率论与数理统计]