The Fractional Quaternion Fourier Number Transform

In this paper, we define a fractional version of the quaternion Fourier number transform (QFNT). With this purpose, we first study the eigenstructure of the QFNT; this is used to obtain the eigendecomposition of the corresponding transform matrix, from which the fractional QFNT can be computed. A multiple parameter version of this transform is then employed to perform encryption of color images. Preliminary results suggest that the proposed scheme is secure, while allowing to deal with all color channels in a holistic manner and take into account possible interactions between them.