Recovery of Sparse Signals Using Multiple Orthogonal Least Squares

We study the problem of sparse recovery from compressed measurements. This problem has generated a great deal of interest in recent years. To recover the sparse signal, we propose a new method called multiple orthogonal least squares (MOLS), which extends the well-known orthogonal least squares (OLS) algorithm by choosing multiple $L$ indices per iteration. Due to the inclusion of multiple support indices in each selection, the MOLS algorithm converges in much fewer iterations and hence improves the computational efficiency over the OLS algorithm. Theoretical analysis shows that MOLS performs the exact recovery of any $K$-sparse signal within $K$ iterations if the measurement matrix satisfies the restricted isometry property (RIP) with isometry constant $\delta_{LK} \leq \frac{\sqrt{L}}{\sqrt{K} + \sqrt{5 L}}.$ Empirical experiments demonstrate that MOLS is very competitive in recovering sparse signals compared to the state of the art recovery algorithms.