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Greedy pursuit, which includes matching pursuit (MP) and orthogonal matching pursuit (OMP), is an efficient approach for sparse approximation. However, conventional greedy pursuit algorithms designed for inner product space are not robust against outliers. In this paper, we devise a new definition of correlation in lp-space with p > 0, called lp-correlation, and introduce the concept of orthogonality in lp-space. Based on the lp-correlation and lp-orthogonality, which are generalizations of the absolute inner product and orthogonality of inner product space, respectively, we develop three greedy pursuit algorithms, namely, lp-MP, lp-OMP, and weak lp-MP, for robust sparse approximation in the presence of outliers. The convergence of the three algorithms is proved. In particular, the lp-norm of the residual of each algorithm decays exponentially. It is revealed that the exponential decay factor in the worst case is related …