Double-encrypted watermarking algorithm based on cosine transform and fractional Fourier transform in invariant wavelet domain

The existing watermarking algorithms invariant wavelet domain are weak at resisting geometric attacks and have small embedding capacities. In this paper, a robust double-encrypted watermarking algorithm based on the fractional Fourier transform (FRFT) and discrete cosine transform (DCT) in invariant wavelet domain is proposed. A hybrid domain is obtained by applying the redistributed invariant wavelet transform (RIDWT) and cosine transform to the enlarged host image. The low-frequency and high-frequency regions of the domain have advantages against different attacks; thus, the two components are both selected for watermark embedding. To solve the false positive problem, the enlarged watermark is double-encrypted by the Arnold transform and the FRFT before a singular value decomposition is applied to it, which enhances the security of the algorithm due to the generation of more keys. Multiparameter particle swarm optimization (MP-PSO) is used to obtain the optimal embedding factors for achieving the balance between invisibility and robustness. The simulation results and comparative experiments show that the proposed algorithm exhibits high robustness under the premise of satisfying security, reliability and invisibility, especially for geometric attacks such as rotation, cropping and translation.