A class of heavy-tailed multivariate non-Gaussian probability models for wavelet coefficients

Fei Shi; Ivan W. Selesnick

doi:10.1117/12.504644

13 November 2003 A class of heavy-tailed multivariate non-Gaussian probability models for wavelet coefficients

Fei Shi, Ivan W. Selesnick

Proceedings Volume 5207, Wavelets: Applications in Signal and Image Processing X; (2003) https://doi.org/10.1117/12.504644
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

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 a N-element vector of wavelet coefficients and ||w|| is a convex combination of l₂ 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.

Citation Download Citation

Fei Shi and Ivan W. Selesnick "A class of heavy-tailed multivariate non-Gaussian probability models for wavelet coefficients", Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); https://doi.org/10.1117/12.504644

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