The DOI matches its Crossref record.
Sparsity and incoherence in compressive sampling
Open accessAbstract
We consider the problem of reconstructing a sparse signal from a limited number of linear measurements. Given m randomly selected samples of Ux 0 , where U is an orthonormal matrix, we show that ℓ 1 minimization recovers x 0 exactly when the number of measurements exceeds where S is the number of nonzero components in x 0 and μ is the largest entry in U properly normalized: . The smaller μ is, the fewer samples needed. The result holds for 'most' sparse signals x 0 supported on a fixed (but arbitrary) set T . Given T , if the sign of x 0 for each nonzero entry on T and the observed values of Ux 0 are drawn at random, the signal is recovered with overwhelming probability. Moreover, there is a sense in which this is nearly optimal since any method succeeding with the same probability would require just about as many samples.
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
An Introduction To Compressive Sampling
Candes, E. J., & Wakin, M. B. (2008) · IEEE Signal Processing Magazine · doi:10.1109/msp.2007.914731 · Cited by 10,017
Exact Matrix Completion via Convex Optimization
Candès, E. J., & Recht, B. (2009) · Foundations of Computational Mathematics · doi:10.1007/s10208-009-9045-5 · Cited by 4,877
Self-citationHyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Bioucas-Dias, J. M., Plaza, A., Dobigeon, N., Parente, M., Du, Q., Gader, P., & Chanussot, J. (2012) · IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing · doi:10.1109/jstars.2012.2194696 · Cited by 2,836
Hyperspectral remote sensing data analysis and future challenges
Bioucas-Dias, J. M., Plaza, A., Camps-Valls, G., Scheunders, P., Nasrabadi, N., & Chanussot, J. (2013) · IEEE Geoscience and Remote Sensing Magazine · doi:10.1109/mgrs.2013.2244672 · Cited by 2,223
Iteratively reweighted algorithms for compressive sensing
Chartrand, R., & Yin, W. (2008) · 2008 IEEE International Conference on Acoustics, Speech and Signal Processing · doi:10.1109/icassp.2008.4518498 · Cited by 1,248
Metadata
- Authors
- Candès, E., & Romberg, J.
- Venue
- Inverse Problems
- Publisher
- IOP Publishing
- Published
- 2007-04-10
- Volume
- 23
- Issue
- 3
- Pages
- 969-985
- ISSN
- 0266-5611 (ISSN-L)
- 1361-6420
- OpenAlex
- W2109357213
- Cited by
- 2,075
- References
- 0
- FWCI
- 83.01
- Type
- journal article
- Language
- en
- Open access
- bronze
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
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Sparsity and incoherence in compressive sampling. https://app.cochat.ai/papers/10.1088/0266-5611/23/3/008
- The paper
- Candès, E., & Romberg, J. (2007). Sparsity and incoherence in compressive sampling. Inverse Problems. https://doi.org/10.1088/0266-5611/23/3/008
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.
