### Abstract

It is well documented that the statistical distribution of wavelet coefficients for natural images is non-Gaussian and that neighboring coefficients are highly dependent. In this paper, we propose a new multivariate non-Gaussian probability model to capture the dependencies among neighboring wavelet coefficients in the same scale. The model can be expressed as K exp(-||w||) where w is an N-element vector of wavelet coefficients and ||w|| is a convex combination of l
_{2} norms over subspaces of R
_{N}. This model includes the commonly used independent Laplacian model as a special case but it has many more degrees of freedom. Based on this model, the corresponding non-linear threshold (shrinkage) function for denoising is derived using Bayesian estimation theory. Although this function does not have a closed-form solution, a successive substitution method can be used to numerically compute it.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Editors | M.A. Unser, A. Aldroubi, A.F. Laine |

Pages | 1-8 |

Number of pages | 8 |

Volume | 5207 |

Edition | 1 |

State | Published - 2003 |

Event | Wavelets: Applications in Signal and Image Processing X - San Diego, CA, United States Duration: Aug 4 2003 → Aug 8 2003 |

### Other

Other | Wavelets: Applications in Signal and Image Processing X |
---|---|

Country | United States |

City | San Diego, CA |

Period | 8/4/03 → 8/8/03 |

### Fingerprint

### Keywords

- Denoising
- Non-Gaussian
- Statistical model
- Wavelet

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*(1 ed., Vol. 5207, pp. 1-8)

**A Class of Heavy-tailed Multivariate Non-Gaussian Probability Models for Wavelet Coefficients.** / Shi, Fei; Selesnick, Ivan.

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

*Proceedings of SPIE - The International Society for Optical Engineering.*1 edn, vol. 5207, pp. 1-8, Wavelets: Applications in Signal and Image Processing X, San Diego, CA, United States, 8/4/03.

}

TY - GEN

T1 - A Class of Heavy-tailed Multivariate Non-Gaussian Probability Models for Wavelet Coefficients

AU - Shi, Fei

AU - Selesnick, Ivan

PY - 2003

Y1 - 2003

N2 - It is well documented that the statistical distribution of wavelet coefficients for natural images is non-Gaussian and that neighboring coefficients are highly dependent. In this paper, we propose a new multivariate non-Gaussian probability model to capture the dependencies among neighboring wavelet coefficients in the same scale. The model can be expressed as K exp(-||w||) where w is an N-element vector of wavelet coefficients and ||w|| is a convex combination of l 2 norms over subspaces of R N. This model includes the commonly used independent Laplacian model as a special case but it has many more degrees of freedom. Based on this model, the corresponding non-linear threshold (shrinkage) function for denoising is derived using Bayesian estimation theory. Although this function does not have a closed-form solution, a successive substitution method can be used to numerically compute it.

AB - It is well documented that the statistical distribution of wavelet coefficients for natural images is non-Gaussian and that neighboring coefficients are highly dependent. In this paper, we propose a new multivariate non-Gaussian probability model to capture the dependencies among neighboring wavelet coefficients in the same scale. The model can be expressed as K exp(-||w||) where w is an N-element vector of wavelet coefficients and ||w|| is a convex combination of l 2 norms over subspaces of R N. This model includes the commonly used independent Laplacian model as a special case but it has many more degrees of freedom. Based on this model, the corresponding non-linear threshold (shrinkage) function for denoising is derived using Bayesian estimation theory. Although this function does not have a closed-form solution, a successive substitution method can be used to numerically compute it.

KW - Denoising

KW - Non-Gaussian

KW - Statistical model

KW - Wavelet

UR - http://www.scopus.com/inward/record.url?scp=1242330935&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1242330935&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:1242330935

VL - 5207

SP - 1

EP - 8

BT - Proceedings of SPIE - The International Society for Optical Engineering

A2 - Unser, M.A.

A2 - Aldroubi, A.

A2 - Laine, A.F.

ER -