Matching Pursuit (MP) aims at finding sparse decompositions of signals over redundant bases of elementary waveforms. Traditionally, MP has been considered too slow an algorithm to be applied to real-life problems with high-dimensional signals. Indeed, in terms of floating points operations, its typical numerical implementations have a complexity of O(N^2) and are associated with impractical runtimes. In this paper, we propose a new architecture which exploits the structure shared by many redundant MP dictionaries, and thus decreases its complexity to O(N log N). This architecture is implemented in a new software toolkit, called MPTK (the Matching Pursuit Toolkit), which is able to reach, e.g., 0.25 x real time for a typical MP analysis scenario applied to a 1 hour long audio track. This substantial acceleration makes it possible, from now on, to ex- plore and apply MP in the framework of real-life, high-dimensional data processing problems.