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Analysis of a class of nonlinear and non-separable multiscale representations

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Abstract

In this paper, we introduce a particular class of nonlinear and non-separable multiscale representations which embeds most of these representations. After motivating the introduction of such a class on one-dimensional examples, we investigate the multi-dimensional and non-separable case where the scaling factor is given by a non-diagonal dilation matrix M. We also propose new convergence and stability results in L p and Besov spaces for that class of nonlinear and non-separable multiscale representations. We end the paper with an application of the proposed study to the convergence and the stability of some nonlinear multiscale representations.

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Authors and Affiliations

  1. LAGA Laboratory, Paris XIII University, Villetaneuse, France

    Basarab Mateï

  2. LJK Laboratory, University of Grenoble, Grenoble, France

    Sylvain Meignen

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  1. Basarab Mateï
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  2. Sylvain Meignen
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Correspondence to Sylvain Meignen.

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Mateï, B., Meignen, S. Analysis of a class of nonlinear and non-separable multiscale representations. Numer Algor 60, 391–418 (2012). https://doi.org/10.1007/s11075-011-9520-3

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  • DOI: https://doi.org/10.1007/s11075-011-9520-3

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