Abstract
Sparse signal models arise commonly in audio and image processing. Recent work in the area of compressed sensing has provided estimates of the performance of certain widely-used sparse signal processing techniques such as basis pursuit and matching pursuit. However, the optimal achievable performance with sparse signal approximation remains unknown. This paper provides bounds on the ability to estimate a sparse signal in noise. Specifically, we show that there is a critical minimum signal-to-noise ratio (SNR) that is required for reliable detection of the sparsity pattern of the signal. We furthermore relate this critical SNR to the asymptotic mean squared error of the maximum likelihood estimate of a sparse signal in additive Gaussian noise. The critical SNR is a simple function of the problem dimensions.
| Original language | English (US) |
|---|---|
| Title of host publication | 2007 IEEE/SP 14th Workshop on Statistical Signal Processing, SSP 2007, Proceedings |
| Pages | 254-258 |
| Number of pages | 5 |
| DOIs | |
| State | Published - 2007 |
| Event | 2007 IEEE/SP 14th WorkShoP on Statistical Signal Processing, SSP 2007 - Madison, WI, United States Duration: Aug 26 2007 → Aug 29 2007 |
Other
| Other | 2007 IEEE/SP 14th WorkShoP on Statistical Signal Processing, SSP 2007 |
|---|---|
| Country | United States |
| City | Madison, WI |
| Period | 8/26/07 → 8/29/07 |
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Keywords
- Basis pursuit
- Compressed sensing
- Estimation
- Matching pursuit
- Maximum likelihood
- Unions of subspaces
ASJC Scopus subject areas
- Signal Processing
Cite this
Rate-distortion bounds for sparse approximation. / Fletcher, Alyson K.; Rangan, Sundeep; Goyal, Vivek K.
2007 IEEE/SP 14th Workshop on Statistical Signal Processing, SSP 2007, Proceedings. 2007. p. 254-258 4301258.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Rate-distortion bounds for sparse approximation
AU - Fletcher, Alyson K.
AU - Rangan, Sundeep
AU - Goyal, Vivek K.
PY - 2007
Y1 - 2007
N2 - Sparse signal models arise commonly in audio and image processing. Recent work in the area of compressed sensing has provided estimates of the performance of certain widely-used sparse signal processing techniques such as basis pursuit and matching pursuit. However, the optimal achievable performance with sparse signal approximation remains unknown. This paper provides bounds on the ability to estimate a sparse signal in noise. Specifically, we show that there is a critical minimum signal-to-noise ratio (SNR) that is required for reliable detection of the sparsity pattern of the signal. We furthermore relate this critical SNR to the asymptotic mean squared error of the maximum likelihood estimate of a sparse signal in additive Gaussian noise. The critical SNR is a simple function of the problem dimensions.
AB - Sparse signal models arise commonly in audio and image processing. Recent work in the area of compressed sensing has provided estimates of the performance of certain widely-used sparse signal processing techniques such as basis pursuit and matching pursuit. However, the optimal achievable performance with sparse signal approximation remains unknown. This paper provides bounds on the ability to estimate a sparse signal in noise. Specifically, we show that there is a critical minimum signal-to-noise ratio (SNR) that is required for reliable detection of the sparsity pattern of the signal. We furthermore relate this critical SNR to the asymptotic mean squared error of the maximum likelihood estimate of a sparse signal in additive Gaussian noise. The critical SNR is a simple function of the problem dimensions.
KW - Basis pursuit
KW - Compressed sensing
KW - Estimation
KW - Matching pursuit
KW - Maximum likelihood
KW - Unions of subspaces
UR - http://www.scopus.com/inward/record.url?scp=47849101498&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=47849101498&partnerID=8YFLogxK
U2 - 10.1109/SSP.2007.4301258
DO - 10.1109/SSP.2007.4301258
M3 - Conference contribution
SN - 142441198X
SN - 9781424411986
SP - 254
EP - 258
BT - 2007 IEEE/SP 14th Workshop on Statistical Signal Processing, SSP 2007, Proceedings
ER -