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|Title:||Singular integrals, scale-space and wavelet transforms||Authors:||Goh, S.S.
Gaussian scale-space and wavelet transforms
Singular integral operators
Wavelets and framelets
|Issue Date:||Dec-2013||Citation:||Goh, S.S., Goodman, T.N.T., Lee, S.L. (2013-12). Singular integrals, scale-space and wavelet transforms. Journal of Approximation Theory 176 : 68-93. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jat.2013.09.007||Abstract:||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 Calderón type inversion formulas, in both integral and semi-discrete forms, are derived for functions in Lp 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. © 2013 Elsevier Inc.||Source Title:||Journal of Approximation Theory||URI:||http://scholarbank.nus.edu.sg/handle/10635/104124||ISSN:||00219045||DOI:||10.1016/j.jat.2013.09.007|
|Appears in Collections:||Staff Publications|
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