Quaternion discrete fractional Krawtchouk transform and its application in color image encryption and watermarking

Abstract

This paper extends the traditional discrete fractional Krawtchouk transform (DFrKT) with quaternion theory to quaternion discrete fractional Krawtchouk transform (QDFrKT) for the purpose of color image processing. Also, the implementation of QDFrKT is given from two points of view, i.e. direct computation and calculation with quaternion symplectic form. The detailed mathematical derivation together with definition and some properties of quaternion algebra are provided. In order to evaluate the applicability of the proposed QDFrKT method, two applications are investigated, including color image encryption and color image watermarking. For color image encryption, experiments are conducted on key sensitivity, histogram analysis, and noise attacks; while for color image watermarking, experiments are conducted on watermarking invisibility and the robustness on attacks of media filter, average filter, Gaussian filter, and geometric attacks. Moreover, with the imperfect decryption property of the encryption algorithm, a potential application of the encryption strategy for designing watermarking algorithm is discussed. The promising experiment results demonstrate the effectiveness and efficiency of our proposed QDFrKT based color image encryption and watermarking techniques.