A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases

B. Adcock; A. Hansen

DOI:10.1007/s00041-012-9221-x

Corpus ID: 10263165

A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases

@article{Adcock2010AGS,
  title={A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases},
  author={B. Adcock and A. Hansen},
  journal={Journal of Fourier Analysis and Applications},
  year={2010},
  volume={18},
  pages={685-716}
}

B. Adcock, A. Hansen

Published 2010

Mathematics, Computer Science

Journal of Fourier Analysis and Applications

We introduce a generalized framework for sampling and reconstruction in separable Hilbert spaces. Specifically, we establish that it is always possible to stably reconstruct a vector in an arbitrary Riesz basis from sufficiently many of its samples in any other Riesz basis. This framework can be viewed as an extension of the well-known consistent reconstruction technique (Eldar et al.). However, whilst the latter imposes stringent assumptions on the reconstruction basis, and may in practice be… CONTINUE READING

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