Improving the bound on the restricted isometry property constant in multiple orthogonal least squares

By allowing multiple L indices to be chosen per iteration, multiple orthogonal least squares (MOLS) have been proposed that is an extension of the classical greedy algorithm OLS. Wang and Li 2017 demonstrated that MOLS can successfully reconstruct K-sparse signals from compressed measurements y = A x in at most K iterations if the sensing matrix A has unit l 2 -norm columns satisfying the restricted isometry property (RIP) of order LK with δ L K < 1 ( K / L ) + 2 . In this study, by increasing the RIP order just by one (i.e. L K + 1 from LK), the authors refine the bound further to δ L K + 1 < ( 1 / ( K / L ) + 2 ) . In the noisy case, they also propose a stopping criterion of MOLS algorithm, and with this criterion MOLS algorithm can recover the support of sparse signal successfully.