An ALPS view of sparse recovery

We provide two compressive sensing (CS) recovery algorithms based on iterative hard-thresholding. The algorithms, collectively dubbed as algebraic pursuits (ALPS), exploit the restricted isometry properties of the CS measurement matrix within the algebra of Nesterov´s optimal gradient methods. We theoretically characterize the approximation guarantees of ALPS for signals that are sparse on ortho-bases as well as on tight-frames. Simulation results demonstrate a great potential for ALPS in terms of phase-transition, noise robustness, and CS reconstruction.