<p>The monogenic signal, as a generalization of the one-dimensional analytic signal to higher-dimensional spaces, has extensive applications in signal feature extraction. This study introduces the monogenic signal associated with Linear Canonical Transform (LCT) and derives the explicit expressions of its Cauchy-Riemann type system in polar form. The LCT-based monogenic signal provides a unique feature representation of a signal by the local complex amplitude and the local complex phase vector. In light of the edge feature information provided by the monogenic signal, we propose two types of image edge detection algorithms based on the amplitude and the phase respectively. Thanks to the flexible and adjustable parameters of LCT, the proposed methods outperform the traditional differential phase congruency method.</p>