Clifford wavelet transform and the associated Donoho-Stark's uncertainty Principle

TL;DR

This paper develops a new uncertainty principle for the continuous Clifford wavelet transform, expanding the theoretical understanding of signal analysis within Clifford algebra frameworks.

Contribution

It introduces a Clifford wavelet-based uncertainty principle, bridging Clifford analysis with wavelet theory for the first time.

Findings

Established a Donoho-Stark type uncertainty principle for Clifford wavelet transform

Reviewed key properties of Clifford algebra and wavelet transforms

Provided theoretical foundations for future applications in signal processing

Abstract

This paper focuses on studying the Donoho-Stark's type uncertainty principle for the continuous Clifford wavelet transform. A brief review of Clifford algebra/analysis, Clifford wavelet transform and their properties is conducted. Next, such concepts are applied to develop an uncertainty principle based on Clifford wavelets.