An Interplay of Ridgelet and Linear Canonical Transforms

Abstract

The present study is the first of its kind, aiming to explore the interface between the ridgelet and linear canonical transforms. To begin with, we formulate a family of linear canonical ridgelet waveforms by suitably chirping a one-dimensional wavelet along a specific direction. The construction of novel ridgelet waveforms is demonstrated via a suitable example supported by vivid graphics. Subsequently, we introduce the notion of linear canonical ridgelet transform, which not only embodies the classical ridgelet transform but also yields another new variant of the ridgelet transform based on the fractional Fourier transform. Besides studying all the fundamental properties, we also present an illustrative example on the implementation of the linear canonical ridgelet transform on a bivariate function.