### Abstract

We describe a statistical model for images decomposed in an overcomplete wavelet pyramid. Each coefficient of the pyramid is modeled as the product of two independent random variables: an element of a Gaussian random field, and a hidden multiplier with a marginal log-normal prior. The latter modulates the local variance of the coefficients. We assume subband coefficients are contaminated with additive Gaussian noise of known covariance, and compute a MAP estimate of each multiplier variable based on observation of a local neighborhood of coefficients. Conditioned on this multiplier, we then estimate the subband coefficients with a local Wiener estimator. Unlike previous approaches, we (a) empirically motivate our choice for the prior on the multiplier; (b) use the full covariance of signal and noise in the estimation; (c) include adjacent scales in the conditioning neighborhood. To our knowledge, the results are the best in the literature, both visually and in terms of squared error.

Original language | English (US) |
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Title of host publication | IEEE International Conference on Image Processing |

Pages | 37-40 |

Number of pages | 4 |

Volume | 2 |

State | Published - 2001 |

Event | IEEE International Conference on Image Processing (ICIP) - Thessaloniki, Greece Duration: Oct 7 2001 → Oct 10 2001 |

### Other

Other | IEEE International Conference on Image Processing (ICIP) |
---|---|

Country | Greece |

City | Thessaloniki |

Period | 10/7/01 → 10/10/01 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Vision and Pattern Recognition
- Hardware and Architecture
- Electrical and Electronic Engineering

### Cite this

*IEEE International Conference on Image Processing*(Vol. 2, pp. 37-40)

**Adaptive Wiener denoising using a Gaussian scale mixture model in the wavelet domain.** / Portilla, J.; Strela, V.; Wainwright, M. J.; Simoncelli, Eero.

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

*IEEE International Conference on Image Processing.*vol. 2, pp. 37-40, IEEE International Conference on Image Processing (ICIP), Thessaloniki, Greece, 10/7/01.

}

TY - GEN

T1 - Adaptive Wiener denoising using a Gaussian scale mixture model in the wavelet domain

AU - Portilla, J.

AU - Strela, V.

AU - Wainwright, M. J.

AU - Simoncelli, Eero

PY - 2001

Y1 - 2001

N2 - We describe a statistical model for images decomposed in an overcomplete wavelet pyramid. Each coefficient of the pyramid is modeled as the product of two independent random variables: an element of a Gaussian random field, and a hidden multiplier with a marginal log-normal prior. The latter modulates the local variance of the coefficients. We assume subband coefficients are contaminated with additive Gaussian noise of known covariance, and compute a MAP estimate of each multiplier variable based on observation of a local neighborhood of coefficients. Conditioned on this multiplier, we then estimate the subband coefficients with a local Wiener estimator. Unlike previous approaches, we (a) empirically motivate our choice for the prior on the multiplier; (b) use the full covariance of signal and noise in the estimation; (c) include adjacent scales in the conditioning neighborhood. To our knowledge, the results are the best in the literature, both visually and in terms of squared error.

AB - We describe a statistical model for images decomposed in an overcomplete wavelet pyramid. Each coefficient of the pyramid is modeled as the product of two independent random variables: an element of a Gaussian random field, and a hidden multiplier with a marginal log-normal prior. The latter modulates the local variance of the coefficients. We assume subband coefficients are contaminated with additive Gaussian noise of known covariance, and compute a MAP estimate of each multiplier variable based on observation of a local neighborhood of coefficients. Conditioned on this multiplier, we then estimate the subband coefficients with a local Wiener estimator. Unlike previous approaches, we (a) empirically motivate our choice for the prior on the multiplier; (b) use the full covariance of signal and noise in the estimation; (c) include adjacent scales in the conditioning neighborhood. To our knowledge, the results are the best in the literature, both visually and in terms of squared error.

UR - http://www.scopus.com/inward/record.url?scp=0035168420&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035168420&partnerID=8YFLogxK

M3 - Conference contribution

VL - 2

SP - 37

EP - 40

BT - IEEE International Conference on Image Processing

ER -