Wavelet transforms based on the special affine convolution
Jing Yang, Yingchun Jiang · International Journal of Wavelets Multiresolution and Information Processing · 2025
In this paper, we mainly study the wavelet construction based on the special affine Fourier transform, including the continuous wavelet transform, dyadic wavelet transform and discrete wavelet transform. First, we give a new definition of the continuous special affine wavelets based on the special affine convolution and show that all admissible wavelets in the Fourier transform domain can also be used as special affine wavelet function. Second, the dyadic special affine wavelet transform is defined and the construction of the dyadic dual wavelets for reconstruction is given. Then, the special affine multiresolution analysis and the corresponding discrete special affine wavelets are proposed. Moreover, fast decomposition and reconstruction algorithms based on the special affine convolution are established. Finally, numerical results demonstrate that the proposed special affine wavelet transform has good performance for denoising non-stationary signals and color images.