# Discrete Uncertainty Principle in Quaternion Setting and Application in Signal Reconstruction

## TL;DR

This paper explores the discrete uncertainty principle within the quaternion Fourier transform framework, demonstrating how sparsity can facilitate the recovery of missing frequency components in signals.

## Contribution

It introduces a novel uncertainty principle for discrete signals in the quaternion setting and applies it to signal reconstruction.

## Key findings

- Sparsity aids in recovering missing frequency information.
- The quaternion uncertainty principle extends classical concepts to new signal domains.
- Application to signal reconstruction shows improved recovery capabilities.

## Abstract

In this paper, the uncertainty principle of discrete signals associated with Quaternion Fourier transform is investigated. It suggests how sparsity helps in the recovery of missing frequency.