Sparse Representations for Signal Processing and Coding

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This project will investigate novel methods to represent signals in a compact and efficient digital format. These methods will be based on the paradigm of finding representations of a signal with a small number of components taken from a large set of elementary functions. Such representations can be used to efficiently store and transmit data such as music, images or video. Furthermore, these representations are able to uncover structure present in the signal under investigation, such as for example notes in music or edges in images. The main focus of this project will lie in the investigation of the theoretical properties of such representations and will build these foundations for the exploitation of such methods in further research. In addition, we will study two specific tasks for which these representations seem ideally suited: the problem of audio coding, that is, representing audio data in a compact and efficient format, and the problem of source separation, that is, extracting the signal associated with a single source such as a speaker from one or more mixtures of many different signals.