Fractional Fourier Transforms Meet Riesz Potentials and Image Processing

SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 476-500, March 2024.
Abstract.Via chirp functions from fractional Fourier transforms, we introduce fractional Riesz potentials related to chirp functions, which are further used to give a new image encryption method with double phase coding. In a comparison with the image encryption method based on fractional Fourier transforms, via a series of image encryption and decryption experiments, we demonstrate that the symbols of fractional Riesz potentials related to chirp functions and the order of fractional Fourier transforms essentially provide greater flexibility and information security. We also establish the relations of fractional Riesz potentials related to chirp functions with fractional Fourier transforms, fractional Laplace operators, and fractional Riesz transforms, and we obtain their boundedness on rotation invariant spaces.