摘要
修正的多重正交最小二乘(modified multiple orthogonal least squares,m^(2)OLS)算法是在多重正交最小二乘算法(multiple orthogonal least squares,m OLS)的基础上提出的.利用m^(2)OLS算法能够从模型y=Ax+v中重构稀疏信号x.借助预选取规则,m^(2)OLS算法的复杂度低于m OLS.在三类噪声干扰下,本文给出保证m^(2)OLS算法每次迭代至少选取一个正确指标的充分条件.该条件是在约束等距性质(restricted isometry property,RIP)框架下给出的.在第一次迭代中,本文给出m^(2)OLS算法不能选取正确指标的条件.与现有的结果相比,本文中的结果具有一定优势.
Based on the multiple orthogonal least squares(mOLS),the modified mOLS(m^(2)OLS)has been proposed to recover the support of sparse signals x from y=Ax+v.By using a pre-selected subset of columns of A,m^(2)OLS can realize computational simplicity over mOLS.In the framework of restricted isometry property(RIP),under three kinds of noise,we present some sufficient conditions on RIP and the minimum magnitude of the nonzero elements of the sparse coefficients,which can guarantee that m^(2)OLS identifies at least one index in the support of any sparse signal in each iteration in the noisy case.We also present a condition under which m^(2)OLS fails to recover the support of x at the first iteration.Our results are better than the existing results.
作者
李海锋
谌稳固
温金明
Haifeng Li;Wengu Chen;Jinming Wen
出处
《中国科学：数学》
CSCD
北大核心
2021年第9期1451-1460,共10页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:61907014,11871109,11871248,11701410和61901160)
博士后基金(批准号:2019M660557)
河南省重点研发与推广专项(批准号:192102310448)
河南师范大学青年基金(批准号:2019QK03)
中国工程物理研究院创新发展基金(批准号:CX20200027)资助项目。
关键词
压缩感知
正交最小二乘
约束等距性质
compressed sensing
orthogonal least squares
restricted isometry property
