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• W1843401079 abstract "Sampling theory has traditionally drawn tools from functional and complex analysis. Past successes, such as the Shannon-Nyquist theorem and recent advances in frame theory, have relied heavily on the application of geometry and analysis. The reliance on geometry and analysis means that these results are dependent on the symmetries of the space of samples. There is a subtle interplay between the topology of the domain of the functions being sampled, and the class of functions themselves. Bandlimited functions are somewhat limiting; often one wishes to sample from other classes of functions. The correct topological tool for modeling all of these situations is the sheaf; a tool which allows local structure and consistency to derive global inferences. This chapter develops a general sampling theory for sheaves using the language of exact sequences, recovering the Shannon-Nyquist theorem as a special case. It presents sheaf-theoretic approach by solving several different sampling problems involving non-bandlimited functions. The solution to these problems show that the topology of the domain has a varying level of importance depending on the class of functions and the specific sampling question being studied." @default.
• W1843401079 created "2016-06-24" @default.
• W1843401079 creator A5032354259 @default.
• W1843401079 date "2015-01-01" @default.
• W1843401079 modified "2023-10-16" @default.
• W1843401079 title "A Sheaf-Theoretic Perspective on Sampling" @default.
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• W1843401079 doi "https://doi.org/10.1007/978-3-319-19749-4_10" @default.
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