Beyond consistent reconstructions: optimality and sharp bounds for generalized sampling, and application to the uniform resampling problem

@article{Adcock2013BeyondCR,
  title={Beyond consistent reconstructions: optimality and sharp bounds for generalized sampling, and application to the uniform resampling problem},
  author={Ben Adcock and Anders C. Hansen and Clarice Poon},
  journal={SIAM J. Math. Analysis},
  year={2013},
  volume={45},
  pages={3132-3167}
}
Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. It allows one to recover any element in any finite-dimensional subspace given finitely many of its samples with respect to an arbitrary basis or frame. Unlike more common approaches for this problem, such as the consistent reconstruction technique of Eldar et al., it leads to numerical methods possessing both guaranteed stability and accuracy. The purpose of this paper is… CONTINUE READING
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