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Greedy methods are often the only practical way to solve very large sparse approximation problems. Among such methods, matching pursuit (MP) is undoubtedly one of the most widely used, due to its simplicity and relatively low overhead. Since MP works sequentially, however, it is not straightforward to formulate it as a parallel algorithm, to take advantage of multicore platforms for real-time processing. In this article, we investigate how a slight modification of MP makes it possible to break down the decomposition into multiple local tasks, while avoiding blocking effects. Our simulations on audio signals indicate that this parallel local matching pursuit (PLoMP) gives results comparable to the original MP algorithm but could potentially run in a fraction of the time-on-the-fly sparse approximations of high-dimensional signals should soon become a reality.