Matching pursuit decomposes a signal into a linear expansion of functions selected from a redundant dictionary, isolating the signal structures that are coherent with respect to a given dictionary. In this paper we focus on the Matching Pursuit representation of the displaced frame difference (dfd). In particular, we introduce a new dictionary for matching pursuit that efficiently exploits the signal structures of the dfd. We also propose a fast strategy to find the atoms exploiting the maximum of the absolute value of the error in the motion predicted image and the convergence of the MSE with the rotation of the atoms. Results show that the fast strategy is quite robust when compared to exhaustive search techniques and it improves the results of a suboptimal search strategy based on a genetic algorithm.