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
Figures and Topics from this paper
68 Citations
Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem
- Computer Science, Mathematics
- SIAM J. Math. Anal.
- 2013
- 56
- PDF
Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon
- Mathematics
- 2010
- 51
- PDF
Generalized Sampling and Infinite-Dimensional Compressed Sensing
- Mathematics, Computer Science
- Found. Comput. Math.
- 2016
- 126
- PDF
Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients
- Mathematics, Computer Science
- Math. Comput.
- 2015
- 12
- PDF
References
SHOWING 1-10 OF 44 REFERENCES
Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon
- Mathematics
- 2010
- 51
- PDF
General Framework for Consistent Sampling in Hilbert Spaces
- Mathematics, Computer Science
- Int. J. Wavelets Multiresolution Inf. Process.
- 2005
- 62
- Highly Influential
Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces: The $L^p$-theory
- Mathematics
- 1998
- 136
- PDF
Sampling with Arbitrary Sampling and
Reconstruction Spaces and Oblique Dual Frame Vectors
- Mathematics
- 2003
- 179
- PDF
Sampling Without Input Constraints: Consistent Reconstruction in Arbitrary Spaces
- Mathematics
- 2004
- 69
- Highly Influential
A general sampling theory for nonideal acquisition devices
- Mathematics, Computer Science
- IEEE Trans. Signal Process.
- 1994
- 394
- Highly Influential