کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4607187 | 1631434 | 2013 | 26 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Singular integrals, scale-space and wavelet transforms Singular integrals, scale-space and wavelet transforms](/preview/png/4607187.png)
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 LpLp 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 BB-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 BB-spline or the spline framelets of Ron and Shen as mother wavelets.
Journal: Journal of Approximation Theory - Volume 176, December 2013, Pages 68–93