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Sparse Sampling: Variations on a Theme by Shannon

Sparse Sampling: Variations on a Theme by Shannon

This video was recorded at Emerging Trends in Visual Computing. Sampling is not only a beautiful topic in harmonic analysis, with an interesting history, but also a subject with high practical impact, at the heart of signal processing and communications and their applications. The question is very simple: when is there a one-to-one relationship between a continuous-time function and adequately acquired samples of this function? A cornerstone result is of course Shannon's sampling theorem, which gives a sufficient condition for reconstructing the projection of a signal onto the subspace of bandlimited functions, and this by taking inner products with a sinc function and its shifts. Many variations of this basic framework exist, and they are all related to a subspace structure of the classes... Show More

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