The multiple-parameter weighted fractional Fourier transform and its application to image encryption

In this paper, we generalize the weighted fractional Fourier transform (WFRFT) to contain one vector parameter N∈ℤ^M, which is denoted by the Multiple-parameter weighted Fractional Fourier Transform (MPWFRFT). The proposed MPWFRFT is shown to possess all of the desired properties for FRFT and it also provides a unified framework for the study of FRFT. In fact, the MPWFRFT will reduce to Zhu´s MFRFT when parameter vector N is an ordinary zero vector. The eigen-relationships between MPWFRFT and other FRFT definitions are also discussed. To give an example of application, we exploit its multiple-parameter feature and propose the double random phase encoding in the MPWFRFT domain for digital image encryption. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.