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CORR
2010
Springer

A Generalized Sampling Theorem for Reconstructions in Arbitrary Bases

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A Generalized Sampling Theorem for Reconstructions in Arbitrary Bases
—We present a generalized sampling theorem allowing reconstructions in arbitrary bases. The classical Shannon Sampling Theorem is a special case of our theorem. Specifically, we establish that it is always possible to recover a function in another basis from sufficiently many samples of its Fourier transform. Thus, given additional information, regularity or sparsity, for example, we may obtain a better reconstruction than that given by the classical approach. Numerical examples are given detailing this procedure.
Ben Adcock, Anders C. Hansen
Added 24 Jan 2011
Updated 24 Jan 2011
Type Journal
Year 2010
Where CORR
Authors Ben Adcock, Anders C. Hansen
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