Tensor product multiresolution analysis with error control for compact image representation

  • Authors:

  • Sergio Amat;Francesc Aràndiga;Albert Cohen;Rosa Donat

  • Affiliations:

  • Departament de Matemàtica Aplicada, Universitat de València, Spain;Departament de Matemàtica Aplicada, Universitat de València, Spain;Laboratoire d'Analyse Numerique, Université Pierre et Marie Curie, 16, rue Clisson, 75013 Paris, France;Departament de Matemàtica Aplicada, Universitat de València, Spain

  • Venue:
  • Signal Processing
  • Year:
  • 2002

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Abstract

A class of multiresolution representations based on nonlinear prediction is studied in the multivariate context based on tensor product strategies. In contrast to standard linear wavelet transforms, these representations cannot be thought of as a change of basis, and the error induced by thresholding or quantizing the coefficients requires a different analysis. We propose specific error control algorithms which ensure a prescribed accuracy in various norms when performing such operations on the coefficients. These algorithms are compared with standard thresholding, for synthetic and real images.