摘要
In countless applications,we need to reconstruct a K-sparse signal x∈R n from noisy measurements y=Φx+v,whereΦ∈R^(m×n)is a sensing matrix and v∈R m is a noise vector.Orthogonal least squares(OLS),which selects at each step the column that results in the most significant decrease in the residual power,is one of the most popular sparse recovery algorithms.In this paper,we investigate the number of iterations required for recovering x with the OLS algorithm.We show that OLS provides a stable reconstruction of all K-sparse signals x in[2.8K]iterations provided thatΦsatisfies the restricted isometry property(RIP).Our result provides a better recovery bound and fewer number of required iterations than those proposed by Foucart in 2013.
基金
supported by the National Natural Science Foundation of China(grant nos.61907014,11871248,11701410,61901160)
the Natural Science Foundation of Guangdong province(No.2021A1515010857)
Youth Science Foundation of Henan Normal University(grant no.2019QK03)
China Postdoctoral Science Foundation(grant no.2019M660557)
Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2019).
