Multiparameter discrete transforms based on discrete orthogonal polynomials and their application to image watermarking

Abstract

Applications of discrete orthogonal polynomials (DOPs) in image processing have been recently emerging. In particular, Krawtchouk, Chebyshev, and Charlier DOPs have been applied as bases for image analysis in the frequency domain. However, fast realizations and fractional-type generalizations of DOP-based discrete transforms have been rarely addressed. In this paper, we introduce families of multiparameter discrete fractional transforms via orthogonal spectral decomposition based on Krawtchouk, Chebyshev, and Charlier DOPs. The eigenvalues are chosen arbitrarily in both unitary and non-unitary settings. All families of transforms, for varieties of eigenvalues, are applied in image watermarking. We also exploit recently introduced fast techniques to reduce complexity for the Krawtchouk case. Experimental results show the robustness of the proposed transforms against watermarking attacks.