Please use this identifier to cite or link to this item:
|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|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Nov 18, 2019
WEB OF SCIENCETM
checked on Nov 11, 2019
checked on Nov 9, 2019
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.