Some results on the denoising problem in the elliptically distributed context

  • Authors:

  • Steeve Zozor;Christophe Vignat

  • Affiliations:

  • Grenoble Laboratory of Images, Speech, Signal and Automatics, Department of Images and Signals, Saint Martin d'Hères, France;L. S. S, Gif-sur-Yvette, France and University of Orsay, France Institut Gaspard Monge, University of Marne-la-Vallée, Marne-la-Vallée, France

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2010

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Abstract

The purpose of this paper is to revisit the denoising problem of a multivariate elliptically symmetric random vector corrupted by a multivariate elliptically symmetric noise. The investigation begins with a review of multivariate elliptically distributed random vectors and of their basic but important properties. A focus is made on the Gaussian scale mixtures, a subclass of the elliptical distributions. In the second part, the denoising problem is revisited in this elliptical context following two classical directions: the minimum mean square error and the maximum a posteriori estimation approaches. Although subject to some restrictions, this investigation extends the two recent studies by Alecu et al. and Selesnick. The practical use of the proposed estimators and some possible special behaviors are then discussed through various illustrative examples.