### Abstract

In this paper, we are interested in modeling groups of wavelet coefficients using a zero-mean, ellipticallycontoured multivariate Laplace probability distribution function (pdf). Specifically, we are interested in the problem of estimating a d-point Laplace vector, s, in additive white Gaussian noise (AWGN), n, from an observation, y = s + n. In the scalar case (d = 1), the MAP and MMSE estimators are already known; and in the vector case (d > 1), the MAP estimator can be obtained by an iterative successive substitution algorithm. For the special case where the contour of the Laplace pdf is spherical, the MMSE estimators for the vector case (d > 1) have been derived in our previous work; we have shown that the MMSE estimator can be expressed in terms of the generalized incomplete Gamma function. For the general ellipticallycontoured case, the MMSE estimator can not be expressed as such. In this paper, we therefore investigate approximations to the MMSE estimator of a Laplace vector in AWGN.

Original language | English (US) |
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Title of host publication | Wavelets XII |

Volume | 6701 |

DOIs | |

State | Published - 2007 |

Event | Wavelets XII - San Diego, CA, United States Duration: Aug 26 2007 → Aug 29 2007 |

### Other

Other | Wavelets XII |
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Country | United States |

City | San Diego, CA |

Period | 8/26/07 → 8/29/07 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics

### Cite this

*Wavelets XII*(Vol. 6701). [67011K] https://doi.org/10.1117/12.736047

**Modeling and estimation of wavelet coefficients using elliptically- contoured multivariate laplace vectors.** / Selesnick, Ivan.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Wavelets XII.*vol. 6701, 67011K, Wavelets XII, San Diego, CA, United States, 8/26/07. https://doi.org/10.1117/12.736047

}

TY - GEN

T1 - Modeling and estimation of wavelet coefficients using elliptically- contoured multivariate laplace vectors

AU - Selesnick, Ivan

PY - 2007

Y1 - 2007

N2 - In this paper, we are interested in modeling groups of wavelet coefficients using a zero-mean, ellipticallycontoured multivariate Laplace probability distribution function (pdf). Specifically, we are interested in the problem of estimating a d-point Laplace vector, s, in additive white Gaussian noise (AWGN), n, from an observation, y = s + n. In the scalar case (d = 1), the MAP and MMSE estimators are already known; and in the vector case (d > 1), the MAP estimator can be obtained by an iterative successive substitution algorithm. For the special case where the contour of the Laplace pdf is spherical, the MMSE estimators for the vector case (d > 1) have been derived in our previous work; we have shown that the MMSE estimator can be expressed in terms of the generalized incomplete Gamma function. For the general ellipticallycontoured case, the MMSE estimator can not be expressed as such. In this paper, we therefore investigate approximations to the MMSE estimator of a Laplace vector in AWGN.

AB - In this paper, we are interested in modeling groups of wavelet coefficients using a zero-mean, ellipticallycontoured multivariate Laplace probability distribution function (pdf). Specifically, we are interested in the problem of estimating a d-point Laplace vector, s, in additive white Gaussian noise (AWGN), n, from an observation, y = s + n. In the scalar case (d = 1), the MAP and MMSE estimators are already known; and in the vector case (d > 1), the MAP estimator can be obtained by an iterative successive substitution algorithm. For the special case where the contour of the Laplace pdf is spherical, the MMSE estimators for the vector case (d > 1) have been derived in our previous work; we have shown that the MMSE estimator can be expressed in terms of the generalized incomplete Gamma function. For the general ellipticallycontoured case, the MMSE estimator can not be expressed as such. In this paper, we therefore investigate approximations to the MMSE estimator of a Laplace vector in AWGN.

UR - http://www.scopus.com/inward/record.url?scp=42149119443&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42149119443&partnerID=8YFLogxK

U2 - 10.1117/12.736047

DO - 10.1117/12.736047

M3 - Conference contribution

AN - SCOPUS:42149119443

SN - 9780819468499

VL - 6701

BT - Wavelets XII

ER -