Parametric Monogenic Linear Canonical Wavelet Transform

The article presents a comprehensive exploration of the parametric monogenic linear canonical wavelet transform, a cutting-edge technique in signal processing. It begins by addressing the limitations of traditional two-dimensional wavelet transforms, particularly their lack of directional sensitivity and robustness to noise. The introduction of the monogenic wavelet transform, which incorporates phase information, marks a significant advancement in capturing the directional structure of signals. The article further extends this concept by integrating the linear canonical transform, a generalized integral transform that unifies various time-frequency analysis methods. This integration leads to the development of the parametric monogenic linear canonical wavelet, which offers enhanced flexibility and stability in signal analysis. The transform's properties are meticulously analyzed, highlighting its advantages in handling multi-scale and multi-directional signals. The article also delves into practical applications, demonstrating the transform's potential in image denoising tasks. Through detailed examples and comparative experiments, it showcases the superior performance of the parametric monogenic linear canonical wavelet transform in preserving structural details while effectively suppressing noise. This makes the article a crucial read for those interested in the latest advancements in signal processing and image analysis.