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Wavelet thresholding for some classes of non-Gaussian noise
 

Summary: Wavelet thresholding for some classes
of non-Gaussian noise
A. Antoniadis*, D. Leporini and J.-C. Pesquet
Laboratoire IMAG-LMC, Universite´ Joseph Fourier, B.P. 53, 38041
Grenoble Cedex 09, France and Universite´ de Marne-la-Valle´e, Cite´
Descartes, 5, Boulevard Descartes, Champs sur Marne,
77454 Marne la Valle´e Cedex 2, France
Wavelet shrinkage and thresholding methods constitute a powerful
way to carry out signal denoising, especially when the underlying
signal has a sparse wavelet representation. They are computationally
fast, and automatically adapt to the smoothness of the signal to be
estimated. Nearly minimax properties for simple threshold estimators
over a large class of function spaces and for a wide range of loss
functions were established in a series of papers by Donoho and
Johnstone. The notion behind these wavelet methods is that the
unknown function is well approximated by a function with a relatively
small proportion of nonzero wavelet coefficients. In this paper, we
propose a framework in which this notion of sparseness can be
naturally expressed by a Bayesian model for the wavelet coefficients
of the underlying signal. Our Bayesian formulation is grounded on the

  

Source: Antoniadis, Anestis - Laboratoire Jean Kuntzmann, Université Joseph Fourier

 

Collections: Mathematics