Quantum Radon Transform and Its Application

TL;DR

This paper introduces the quantum Radon transform (QRT), a quantum version of the classical Radon transform, enabling exponentially faster image processing tasks like denoising and line detection with comparable effectiveness.

Contribution

The paper proposes the quantum Radon transform and related algorithms, achieving exponential speedups over classical methods for image denoising and line detection tasks.

Findings

QRT is exponentially faster than classical Radon transform.

QRT maintains denoising capabilities comparable to classical methods.

Quantum algorithms for IDRT and line detection offer polynomial speedups.

Abstract

This paper extends the Radon transform, a classical image processing tool for fast tomography and denoising, to the quantum computing platform. A new kind of periodic discrete Radon transform (PDRT), called quantum Radon transform (QRT), is proposed. The QRT has a quantum implementation that is exponentially faster than the classical Radon transform. Based on the QRT, we design an efficient quantum image denoising algorithm. The simulation results show that QRT preserves the good denoising capability as in the classical PDRT. Also, a quantum algorithm for interpolation-based discrete Radon transform (IDRT) is proposed, which can be used for fast line detection. Both the quantum extension of IDRT and the line detection algorithm can provide polynomial speedups over the classical counterparts.