This paper studies a multiple-measurement vector (MMV)-based sparse regression approach to blind hyperspectral unmixing. In general, sparse regression requires a dictionary. The considered approach uses the measured hyperspectral data as the dictionary, thereby intending to represent the whole measured data using the fewest number of measured hyperspectral vectors. We tackle this self-dictionary MMV (SD-MMV) approach using greedy pursuit. It is shown that the resulting greedy algorithms are identical or very similar to some representative pure pixels identification algorithms, such as vertex component analysis. Hence, our study provides a new dimension on understanding and interpreting pure pixels identification methods. We also prove that in the noiseless case, the greedy SD-MMV algorithms guarantee perfect identification of pure pixels when the pure pixel assumption holds.