The DOI matches its Crossref record; 46 of the 46 references it cites were found in a registry or an index.
Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces
Abstract
This article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift-invariant spaces. It is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shift-invariant subspaces by bringing together wavelet theory, frame theory, reproducing kernel Hilbert spaces, approximation theory, amalgam spaces, and sampling. Inspired by applications taken from communication, astronomy, and medicine, the following aspects will be emphasized: (a) The sampling problem is well defined within the setting of shift-invariant spaces. (b) The general theory works in arbitrary dimension and for a broad class of generators. (c) The reconstruction of a function from any sufficiently dense nonuniform sampling set is obtained by efficient iterative algorithms. These algorithms converge geometrically and are robust in the presence of noise. (d) To model the natural decay conditions of real signals and images, the sampling theory is developed in weighted L p -spaces.
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Cites
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Cited by
Convex Optimization in Signal Processing and Communications
(2009) · Cambridge University Press eBooks · doi:10.1017/cbo9780511804458 · Cited by 554
Designing structured tight frames via an alternating projection method
Tropp, J. A., Dhillon, I. S., Heath, R. W., & Strohmer, T. (2005) · IEEE Transactions on Information Theory · doi:10.1109/tit.2004.839492 · Cited by 494
Synchrosqueezing-Based Recovery of Instantaneous Frequency from Nonuniform Samples
Thakur, G., & Wu, H.-T. (2011) · SIAM Journal on Mathematical Analysis · doi:10.1137/100798818 · Cited by 388
A Theory for Sampling Signals From a Union of Subspaces
Lu, Y. M., & Do, M. N. (2008) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2007.914346 · Cited by 286
Metadata
- Authors
- Aldroubi, A., & Gröchenig, K.
- Venue
- SIAM Review
- Published
- 2001-01
- Volume
- 43
- Issue
- 4
- Pages
- 585-620
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2004421506
- Cited by
- 728
- References
- 46
- FWCI
- 51.26
- Type
- journal article
- Language
- en
- Open access
- closed
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