3-D generalized analytic signal associated with linear canonical transform in Clifford biquaternion domain

TL;DR

This paper introduces a new 3D Clifford biquaternionic analytic signal based on the Clifford linear canonical transform, enhancing envelope detection and visualization of multidimensional signals.

Contribution

It generalizes the Clifford Fourier transform to the CLCT, creating a novel analytic signal for improved 3D image analysis.

Findings

Enhanced envelope detection in 3D images

Better visual appearance of signal features

Demonstrated advantages through synthesis examples

Abstract

The analytic signal is a useful mathematical tool. It separates qualitative and quantitative information of a signal in form of the local phase and local amplitude. The Clifford Fourier transform (CFT) plays a vital role in the representation of multidimensional signals. By generalizing the CFT to the Clifford linear canonical transform (CLCT), we present a new type of Clifford biquaternionic analytic signal. Due to the advantages of more freedom, the envelop detection problems of 3D images, with the help of this new analytic signal, can get a better visual appearance. Synthesis examples are presented to demonstrate these advantages.