The DOI matches its Crossref record.
Sparse representations in unions of bases
Open accessAbstract
The purpose of this correspondence is to generalize a result by Donoho and Huo and Elad and Bruckstein on sparse representations of signals in a union of two orthonormal bases for R/sup N/. We consider general (redundant) dictionaries for R/sup N/, and derive sufficient conditions for having unique sparse representations of signals in such dictionaries. The special case where the dictionary is given by the union of L/spl ges/2 orthonormal bases for R/sup N/ is studied in more detail. In particular, it is proved that the result of Donoho and Huo, concerning the replacement of the /spl lscr//sup 0/ optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may be highly redundant.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Donoho, D. L. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.871582 · Cited by 23,994
Candes, E. J., Romberg, J., & Tao, T. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.862083 · Cited by 15,639
A sparse signal reconstruction perspective for source localization with sensor arrays
Malioutov, D., Cetin, M., & Willsky, A. S. (2005) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2005.850882 · Cited by 2,638
Global and local uncertainty principles for signals on graphs
Perraudin, N., Ricaud, B., Shuman, D. I., & Vandergheynst, P. (2018) · APSIPA Transactions on Signal and Information Processing · doi:10.1017/atsip.2018.2 · Cited by 58
Sparsity-Aware Learning and Compressed Sensing: An Overview
Theodoridis, S., Kopsinis, Y., & Slavakis, K. (2014) · Academic Press Library in Signal Processing · doi:10.1016/b978-0-12-396502-8.00023-1 · Cited by 14
Metadata
- Authors
- Gribonval, R., & Nielsen, M.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2003-12
- Volume
- 49
- Issue
- 12
- Pages
- 3320-3325
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2136235822
- Cited by
- 960
- References
- 0
- FWCI
- 30.42
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
