Multivariate denoising using wavelets and principal component analysis

Authors:
Mina Aminghafari;Nathalie Cheze;Jean-Michel Poggi
Affiliations:
Laboratoire de Mathématique - U.M.R. C 8628, "Probabilités, Statistique et Modélisation", Université Paris-Sud, Bít. 425, 91405 Orsay Cedex, France and Amirkabir Universit ...;Laboratoire de Mathématique - U.M.R. C 8628, "Probabilités, Statistique et Modélisation", Université Paris-Sud, Bít. 425, 91405 Orsay Cedex, France and Université Par ...;Laboratoire de Mathématique - U.M.R. C 8628, "Probabilités, Statistique et Modélisation", Université Paris-Sud, Bít. 425, 91405 Orsay Cedex, France and Université Par ...
Venue:
Computational Statistics & Data Analysis
Year:
2006

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Abstract

A multivariate extension of the well known wavelet denoising procedure widely examined for scalar valued signals, is proposed. It combines a straightforward multivariate generalization of a classical one and principal component analysis. This new procedure exhibits promising behavior on classical bench signals and the associated estimator is found to be near minimax in the one-dimensional sense, for Besov balls. The method is finally illustrated by an application to multichannel neural recordings.