TY - JOUR
T1 - Polar Linear Canonical Wavelet Transform
T2 - Theory and Its Application
AU - Zhao, Hui
AU - Li, Bingzhao
AU - Zhu, Hongmei
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
PY - 2025/8
Y1 - 2025/8
N2 - The polar wavelet transform (PWT) has been proven to be a powerful mathematical tool for signal and image processing in recent years. However, the PWT has some limitations to fully exploit the intrinsic directional features of high-dimensional signals like images. Focusing on this problem, the polar linear canonical wavelet transform (PLCWT) is proposed in this paper. The main goal of this paper is to define PLCWT and investigate its mathematical properties including the inversion formula as well as derive the convolution and correlation theorems of the PLCWT. Finally, a potential application of the PLCWT in medical edge detection is discussed. The ability to detect subtle or weak edges in medical images is the key for accurate early detection and diagnoses. Our numerical experiment demonstrates that the proposed transform PLCWT successfully detects subtle retinal blood vessels of an eye image that were overlooked by both the traditional Canny algorithm and the PWT.
AB - The polar wavelet transform (PWT) has been proven to be a powerful mathematical tool for signal and image processing in recent years. However, the PWT has some limitations to fully exploit the intrinsic directional features of high-dimensional signals like images. Focusing on this problem, the polar linear canonical wavelet transform (PLCWT) is proposed in this paper. The main goal of this paper is to define PLCWT and investigate its mathematical properties including the inversion formula as well as derive the convolution and correlation theorems of the PLCWT. Finally, a potential application of the PLCWT in medical edge detection is discussed. The ability to detect subtle or weak edges in medical images is the key for accurate early detection and diagnoses. Our numerical experiment demonstrates that the proposed transform PLCWT successfully detects subtle retinal blood vessels of an eye image that were overlooked by both the traditional Canny algorithm and the PWT.
KW - Convolution theorem
KW - Edge detection
KW - Linear canonical transform
KW - Polar linear canonical wavelet transform
KW - Polar wavelet transform
UR - https://www.scopus.com/pages/publications/105002726876
U2 - 10.1007/s00034-025-03085-x
DO - 10.1007/s00034-025-03085-x
M3 - Article
AN - SCOPUS:105002726876
SN - 0278-081X
VL - 44
SP - 6056
EP - 6078
JO - Circuits, Systems, and Signal Processing
JF - Circuits, Systems, and Signal Processing
IS - 8
ER -