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In this paper a novel greedy algorithm, called least squares orthogonal pursuit (LSOP), is proposed to solve the sparse approximation problem in practical compressive sensing. Unlike orthogonal matching pursuit (OMP) which finds the support set of the unknown signal iteratively with the idea of matching filter, LSOP selects the candidate according to the least squares solution of the residual signal. It is shown that the proposed algorithm surpasses OMP because its coherence statistic is smaller than that of the latter. In addition, the idea that the least squares solution aids support set selection can be extended to all OMP-based algorithms and improves their performances. Several numerical experiments demonstrate that the proposed LSOP family has better behaviors in solving sparse recovery problem than the available OMP family.