Fast least squares pursuits for sparse recovery

We present a new greedy strategy with an efficient implementation technique that enjoys similar computational complexity to OMP. Its recovery performance in the noise free and the Gaussian noise cases is comparable and in many cases better than other existing sparse recovery algorithms both with respect to their theoretical guarantees and empirical reconstruction performance. Our framework has other appealing properties. Convergence is always guaranteed even in the case that the recovery conditions are violated. In addition, our implementation method is useful for improving the computational cost of other methods such as orthogonal least squares (OLS).