JournalsrmiVol. 9, No. 1pp. 51–137

Non-separable bidimensional wavelet bases

  • Albert Cohen

    Université Pierre et Marie Curie, Paris, France
  • Ingrid Daubechies

    Duke University, Durham, USA
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Abstract

We build orthonormal and biorthogonal wavelet bases of L2(R2)L^2(\mathbb R^2) with dilation matrices of determinant 2. As for the one dimensional case, our construction uses a scaling function which solves a two-scale difference equation associated to a FIR filter. Our wavelets are generated from a single cornpactly supported mother function. However, the regularity of these functions cannot be derived by the same approach as in the one dimensional case. We review existing techniques to evaluate the regularity of wavelets, and we introduce new methods which allow to estimate the smoothness of non-separable wavelets and scaling functions in the most general situations. We illustrate these with several examples.

Cite this article

Albert Cohen, Ingrid Daubechies, Non-separable bidimensional wavelet bases. Rev. Mat. Iberoam. 9 (1993), no. 1, pp. 51–137

DOI 10.4171/RMI/133