Sparse linear regression via generalized orthogonal least-squares

The Orthogonal Least Squares (OLS) algorithm sequentially selects columns of the coefficient matrix to greedily find an approximate sparse solution to an underdetermined system of linear equations. In this paper, conditions under which OLS recovers sparse signals from a low number of random linear measurements with probability arbitrarily close to one are stated. Moreover, a computationally efficient generalization of Orthogonal Least-Squares which relies on a recursive relation between the components of the optimal solution to select L columns at each step and solve the resulting overdetermined system of equations is proposed. This generalized OLS algorithm is empirically shown to outperform existing greedy algorithms broadly used in literature.