Singular integrals, scale-space and wavelet transforms
- Autores: Say Song Goh, T. N. T. Goodman, S. L. Lee
- Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 176, Nº 1, 2013, págs. 68-93
- Idioma: inglés
- DOI: 10.1016/j.jat.2013.09.007
- Enlaces
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Resumen
The Gaussian scale-space is a singular integral convolution operator with scaled Gaussian kernel. For a large class of singular integral convolution operators with differentiable kernels, a general method for constructing mother wavelets for continuous wavelet transforms is developed, and Calder´on type inversion formulas, in both integral and semi-discrete forms, are derived for functions in L p spaces. In the case of the Gaussian scale-space, the semi-discrete inversion formula can further be expressed as a sum of wavelet transforms with the even order derivatives of the Gaussian as mother wavelets. Similar results are obtained for B-spline scale-space, in which the high frequency component of a function between two consecutive dyadic scales can be represented as a finite linear combination of wavelet transforms with the derivatives of the B-spline or the spline framelets of Ron and Shen as mother wavelets.
