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Every time the release button of a digital camera is pressed, several megabytes of raw data are recorded. But the size of a typical jpeg output file is only 10% of that. What a waste! Can't we design a process which records only the relevant 10% of the data to begin with? I will give an introduction to the concepts and math of compressed sensing - a theory that achieves this trick for certain signals. A variant of compressed sensing aims to exploit representations of data in terms of low-rank matrices. There has been a fruitful exchange of ideas between this theory and quantum physics. Methods that we had originally introduced in the context of quantum state estimation have since found applications to tasks as diverse as face recognition, the analysis of x-ray diffraction images, and the prediction of user preferences in online shops. Specific quantum information ideas that feature in this context including trace inequalities and their use to prove large deviation bounds for random matrices, phase space methods, and the notion of complex projective designs.

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David Gross, ITP Cologne
TP seminar room 0.03
Contact: not specified