Polar Linear Canonical Wavelet Transform: Theory and Its Application
Abstract
The polar wavelet transform (PWT) has been proven to be a powerful mathematical tool for signal and image processing in recent years. Due to the increasing demand for directional representations of signals in engineering, it is impossible to fully exploit the intrinsic directional features of signals to describe high-dimensional signals like images. Focusing on this problem, the polar linear canonical wavelet transform (PLCWT) is proposed in this paper. Firstly, the theory of the PLCWT is investigated in detail, including its definition, basic properties and inversion formula. Secondly, the convolution and correlation theorems of the PLCWT are derived. Thirdly, uncertainty principles related to the PLCWT are obtained. Finally, the potential application of the PLCWT in image edge detection is discussed. Simulation results verify the correctness and effectiveness of the proposed method.
Keywords
Cite
@article{arxiv.2312.06702,
title = {Polar Linear Canonical Wavelet Transform: Theory and Its Application},
author = {Hui Zhao and Bing-Zhao Li},
journal= {arXiv preprint arXiv:2312.06702},
year = {2023}
}
Comments
33 pages, 7 figures