Fractional Fourier Transforms Meet Riesz Potentials and Image Processing

TL;DR

This paper explores the mathematical foundations of fractional Riesz potentials and transforms related to chirp functions, establishing their properties and demonstrating their application in secure image encryption.

Contribution

It introduces a novel image encryption method based on fractional Riesz potentials related to chirp functions, enhancing security through increased degrees of freedom.

Findings

Established relations between fractional Riesz potentials and Fourier transforms

Demonstrated boundedness on rotation invariant spaces

Developed a new secure image encryption technique

Abstract

Via chirp functions from fractional Fourier transforms, the authors introduce fractional Riesz potentials related to chirp functions, establish their relations with fractional Fourier transforms, fractional Laplace operators related to chirp functions, and fractional Riesz transforms related to chirp functions, and obtain their boundedness on rotation invariant spaces related to chirp functions. Finally, the authors give the numerical image simulation of fractional Riesz potentials related to chirp functions and their applications in image processing. The main novelty of this article is to propose a new image encryption method for the double phase coding based on the fractional Riesz potential related to chirp functions. The symbol of fractional Riesz potentials related to chirp functions essentially provides greater degrees of freedom and greatly makes the information more secure.