基于截断加权基追踪模型的迭代支撑探测算法  

ITERATIVE SUPPORT DETECTION ALGORITHMS BASED ON TRUNCATED REWEIGHTED BASIS PURSUIT MODEL

作　　者：李亚玲[1] 胡宝安[1] 李梅英[1] 

机构地区：[1]军事交通学院基础部数学教研室,天津300161

出　　处：《计算数学》2015年第1期42-56,共15页Mathematica Numerica Sinica

摘　　要：迭代支撑探测算法是基于截断的基追踪(Basis Pursuit,BP)模型的一种l_1最小化信号重构算法,它可以实现信号的快速重构并且所需要的观测值比经典的L1算法以及迭代加权L1算法更少.本文针对非零元具有快速退化分布性质的稀疏信号,提出了一种改进算法一一基于截断的加权BP模型的迭代支撑探测算法.在迭代的过程中,改进的算法探测原信号支撑集中元素的同时调整重构模型的权值,使得重构模型更有利于实现信号的精确重构.根据所考虑的信号的非零元具有快速退化分布性质这样的先验信息,利用阈值法则探测原信号支撑集中的元素.最后通过Matlab数值实验实现了算法,验证了基于截断的加权BP模型的迭代支撑探测算法比迭代加权L1算法需要的观测值更少,并且比迭代加权L1算法以及传统的迭代支撑探测算法需要更少的重构时间就可以实现信号的精确重构.Iterative support detection algorithm（ISD） is an l1 minimization signal reconstruction approach based on truncated basis pursuit（BP） model. Compared to the classical L1 algorithm and the iterative reweighted L1 algorithm, ISD needs fewer measurements and the signal can be recovered quickly. In this paper, we present an improved ISD algorithm based on truncated reweighted BP model for recovering signals with fast decaying distribution of nonzeros from compressive sensing measurements. we introduce the improved ISD algorithm implemented with threshold rule, while values of the weights in reconstruction model are modified during each iteration, aiming to improve the reconstruction model for finding the corrected solution. Numerical experiments show that ISD algorithm based on truncated reweighted BP model needs fewer measurements than iterative reweighted L1 algorithm, and less reconstruction time than both iterative rewcighted L1 algorithm and classical ISD for signal reconstruction exactly.

关 键 词：压缩感知 信号重构 迭代支撑探测算法 阈值 截断的加权BP模型 

分 类 号：O241.6[理学—计算数学]