### 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) |
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Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 5207 |

Issue number | 1 |

DOIs | |

State | Published - 2003 |

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

### Keywords

- Denoising
- Non-Gaussian
- Statistical model
- Wavelet

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering