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}
}

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