Sparse Signal Recovery Using gOMP Assisted mOLS.

Because of fast convergence in finite number of steps and low computational complexity, signal recovery from compressed measurements using greedy algorithms have generated a large amount of interest in recent years. Among these greedy algorithms OMP is well studied and recently its generalization, gOMP, have also drawn attention. On the other hand OLS and its generalization mOLS have been studied in recent years because of their potential advantages in signal recovery guarantee compared to OMP or gOMP. But OLS and mOLS have the shortcomings of high computational complexity. In this paper we propose a new algorithm which uses gOMP to preselect a N length set out of which mOLS selects its L best coefficients. We have shown that our new algorithm, named gOMPamOLS, is guaranteed to reconstruct a K sparse signals perfectly from compressed measurements if the restricted isometry constant satisfies $\delta_{LK+N}<\frac{\sqrt{L}}{\sqrt{L}+\sqrt{K+L}}$ . Moreover experimental results indicate that gOMPamOLS is robust under sensing matrix with correlated dictionary in terms of signal reconstruction and is much faster than OLS.