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.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Ben Adcock, Anders C. Hansen
• Keywords: Arbitrary Bases, CORR 2010, Education, Generalized Sampling, Shannon Sampling Theorem