The DOI matches its Crossref record; 39 of the 39 references it cites were found in a registry or an index.
Compressive Sensing by Random Convolution
Abstract
This paper demonstrates that convolution with random waveform followed by random time-domain subsampling is a universally efficient compressive sensing strategy. We show that an n-dimensional signal which is S-sparse in any fixed orthonormal representation can be recovered from $m\gtrsim S\log n$ samples from its convolution with a pulse whose Fourier transform has unit magnitude and random phase at all frequencies. The time-domain subsampling can be done in one of two ways: in the first, we simply observe m samples of the random convolution; in the second, we break the random convolution into m blocks and summarize each with a single randomized sum. We also discuss several imaging applications where convolution with a random pulse allows us to superresolve fine-scale features, allowing us to recover high-resolution signals from low-resolution measurements.
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Donoho, D. L. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.871582 · Cited by 23,994
Donoho, D. L. (2004) · Cited by 16,703
Candes, E. J., Romberg, J., & Tao, T. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.862083 · Cited by 15,639
Self-citationSignal Recovery From Random Measurements Via Orthogonal Matching Pursuit
Tropp, J. A., & Gilbert, A. C. (2007) · IEEE Transactions on Information Theory · doi:10.1109/tit.2007.909108 · Cited by 9,653
Matching pursuits with time-frequency dictionaries
Mallat, S. G., & Zhang, Z. (1993) · IEEE Transactions on Signal Processing · doi:10.1109/78.258082 · Cited by 9,112
Stable signal recovery from incomplete and inaccurate measurements
Candès, E. J., Romberg, J. K., & Tao, T. (2006) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.20124 · Cited by 7,036
Self-citationAtomic Decomposition by Basis Pursuit
Chen, S. S., Donoho, D. L., & Saunders, M. A. (1998) · SIAM Journal on Scientific Computing · doi:10.1137/s1064827596304010 · Cited by 6,845
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
Candes, E. J., & Tao, T. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.885507 · Cited by 6,839
Probability Inequalities for sums of Bounded Random Variables
Hoeffding, W. (1994) · Springer Series in Statistics · doi:10.1007/978-1-4612-0865-5_26 · Cited by 6,666
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
Needell, D., & Tropp, J. A. (2009) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2008.07.002 · Cited by 4,326
Cited by
Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals
Tropp, J. A., Laska, J. N., Duarte, M. F., Romberg, J. K., & Baraniuk, R. G. (2010) · IEEE Transactions on Information Theory · doi:10.1109/tit.2009.2034811 · Cited by 1,089
Self-citationSignal Processing With Compressive Measurements
Davenport, M. A., Boufounos, P. T., Wakin, M. B., & Baraniuk, R. G. (2010) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2009.2039178 · Cited by 623
Restricted Eigenvalue Properties for Correlated Gaussian Designs
Raskutti, G., Wainwright, M. J., & Yu, B. (2010) · doi:10.5555/1756006.1859929 · Cited by 367
New and Improved Johnson–Lindenstrauss Embeddings via the Restricted Isometry Property
Krahmer, F., & Ward, R. (2011) · SIAM Journal on Mathematical Analysis · doi:10.1137/100810447 · Cited by 290
Metadata
- Authors
- Romberg, J.
- Venue
- SIAM Journal on Imaging Sciences
- Published
- 2009-01
- Volume
- 2
- Issue
- 4
- Pages
- 1098-1128
- ISSN
- 1936-4954 (ISSN-L)
- OpenAlex
- W1966637115
- Cited by
- 458
- References
- 39
- FWCI
- 44.18
- Type
- journal article
- Language
- en
- Open access
- closed
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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.
