Abstract
Wavelet domain statistical modeling of images has focused on modeling the peaked heavy-tailed behavior of the marginal distribution and on modeling the dependencies between coefficients that are adjacent (in location and/or scale). In this paper we describe the extension of the Laplace marginal model to the multivariate case so that groups of wavelet coefficients can be modeled together using Laplace marginal models. We derive the nonlinear MAP and MMSE shrinkage functions for a Laplace vector in Gaussian noise and provide computationally efficient approximations to them. The development depends on the generalized incomplete Gamma function.
| Original language | English (US) |
|---|---|
| Title of host publication | 2006 IEEE International Conference on Image Processing, ICIP 2006 - Proceedings |
| Pages | 2097-2100 |
| Number of pages | 4 |
| DOIs | |
| State | Published - 2006 |
| Event | 2006 IEEE International Conference on Image Processing, ICIP 2006 - Atlanta, GA, United States Duration: Oct 8 2006 → Oct 11 2006 |
Other
| Other | 2006 IEEE International Conference on Image Processing, ICIP 2006 |
|---|---|
| Country | United States |
| City | Atlanta, GA |
| Period | 10/8/06 → 10/11/06 |
Keywords
- Estimation
- Exponential distributions
- Image restoration
- MAP estimation
- Wavelet transforms
ASJC Scopus subject areas
- Software
- Computer Vision and Pattern Recognition
- Signal Processing
Cite this
Laplace random vectors, Gaussian noise, and the generalized incomplete gamma function. / Selesnick, Ivan.
2006 IEEE International Conference on Image Processing, ICIP 2006 - Proceedings. 2006. p. 2097-2100 4106975.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Laplace random vectors, Gaussian noise, and the generalized incomplete gamma function
AU - Selesnick, Ivan
PY - 2006
Y1 - 2006
N2 - Wavelet domain statistical modeling of images has focused on modeling the peaked heavy-tailed behavior of the marginal distribution and on modeling the dependencies between coefficients that are adjacent (in location and/or scale). In this paper we describe the extension of the Laplace marginal model to the multivariate case so that groups of wavelet coefficients can be modeled together using Laplace marginal models. We derive the nonlinear MAP and MMSE shrinkage functions for a Laplace vector in Gaussian noise and provide computationally efficient approximations to them. The development depends on the generalized incomplete Gamma function.
AB - Wavelet domain statistical modeling of images has focused on modeling the peaked heavy-tailed behavior of the marginal distribution and on modeling the dependencies between coefficients that are adjacent (in location and/or scale). In this paper we describe the extension of the Laplace marginal model to the multivariate case so that groups of wavelet coefficients can be modeled together using Laplace marginal models. We derive the nonlinear MAP and MMSE shrinkage functions for a Laplace vector in Gaussian noise and provide computationally efficient approximations to them. The development depends on the generalized incomplete Gamma function.
KW - Estimation
KW - Exponential distributions
KW - Image restoration
KW - MAP estimation
KW - Wavelet transforms
UR - http://www.scopus.com/inward/record.url?scp=78649809636&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78649809636&partnerID=8YFLogxK
U2 - 10.1109/ICIP.2006.312821
DO - 10.1109/ICIP.2006.312821
M3 - Conference contribution
AN - SCOPUS:78649809636
SN - 1424404819
SN - 9781424404810
SP - 2097
EP - 2100
BT - 2006 IEEE International Conference on Image Processing, ICIP 2006 - Proceedings
ER -