Least Squares Pursuit for sparse signal recovery

This paper presents a novel algorithm for sparse signal recovery, named Least Squares Pursuit, based on least-squares minimization followed by choosing the atom with the largest resulting coefficient, in a greedy one-by-one fashion. It follows a similar approach to that of Orthogonal Matching Pursuit, but with different prioritization of the constraints. We propose an efficient implementation for Least Squares Pursuit, derive theoretical guarantees for signal recovery, and finally present promising simulation results.