Fractional Charlier moments for image reconstruction and image watermarking

Abstract

In this paper, we propose a new set of discrete orthogonal polynomials called fractional Charlier polynomials (FrCPs). This new set will be used as a basic function to define the fractional discrete orthogonal Charlier moments (FrCMs). The proposed FrCPs are derived algebraically using the spectral decomposition of Charlier polynomials (CPs), then the Lagrange interpolation formula is used to derive the spectral projectors. Then, each spectral projector matrix is decomposed by the singular value decomposition (SVD) technique in order to build a basic set of orthonormal eigenvectors which help to develop FrCPs. FrCMs are deduced in matrix form from the proposed FrCPs and are applied for image reconstruction and watermarking. The experimental results show the capacity of the FrCMs proposed for image reconstruction and image watermarking against different attacks such as noise and geometric distortions.