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Compressed sensing in infinite dimensions

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Compressed sensing is a great tool for solving inverse problems (in particular in medical imaging), and the mathematical framework relies heavily on delicate tools from statistics. However, the current theory covers only problems in finite dimensions. In this talk I will show how the theory by Candes and Tao can be extended to include problems in infinite dimensions. This allows for recovery of much more general objects including infinite resolution images. The tools required come from probability, operator theory and geometry of Banach spaces, and the emphasis will be on the statistical aspects. I’ll give an introduction to what is already known (accompanied by numerical examples) and discuss some of the open questions.

This talk is part of the Statistics series.

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