A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of *** this paper,we consider the number of iterations required for the MOLS algori...
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A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of *** this paper,we consider the number of iterations required for the MOLS algorithm for recovery of a K-sparse signal x∈R^(n).We show that MOLS provides stable reconstruction of all K-sparse signals x from y=Ax+w in|6K/ M|iterations when the matrix A satisfies the restricted isometry property(RIP)with isometry constantδ_(7K)≤*** with the existing results,our sufficient condition is not related to the sparsity level K.
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 *** least squares(OLS),which selects at each ste...
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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 *** 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 *** this paper,we investigate the number of iterations required for recovering x with the OLS *** 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.
作者：
Shan-qi PANGYa-ping WANGMing-yao AISchool of Mathematics and Information Science
Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal ControlHenan Normal UniversityXinxiang 453007China KLATASDS-MOE
School of StatisticsEast China Normal UniversityShanghai 200062China LMAM
School of Mathematical Sciences and Center for Statistical SciencePeking UniversityBeijing 100871China
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In this paper a new class of orthogonal arrays(OAs),i.e.,OAs without interaction columns,are proposed which are applicable in factor screening,interaction detection and other *** the tools of difference matrices,we present some general recursive methods for constructing OAs of such *** families of OAs with high percent saturation are *** particular,for any integerλ≥3,such a two-level OA of run 4λcan always be obtained if the corresponding Hadamard matrix exists.
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