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The perceptual orthogonal matching pursuit (POMP), a sparse approximation algorithm built upon the known orthogonal matching pursuit (OMP), is introduced. It is designed for speech processing and can be of great use in speech coding applications. It can handle all types of real dictionaries, including predefined and adaptive dictionaries. Being a suboptimal method, POMP performs a series of local updates where it minimises a perceptual distortion measure involving a perceptual weighting filter. This filter is tailored for speech signals and is used in AMR 3GPP coders. Experiments show that POMP outperforms the standard OMP for predefined and adaptive dictionaries.