  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.

General Mathematics