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.

现有的不变小波域水印算法抗几何攻击能力弱，嵌入能力小。提出了一种基于不变小波域的分数阶傅里叶变换（FRFT）和离散余弦变换（DCT）的鲁棒双重加密水印算法。通过将重新分布的不变小波变换（RIDWT）和余弦变换应用于放大后的宿主图像，可以获得混合域。该域的低频和高频区域具有抵御不同攻击的优势；因此，两个分量都被选择用于水印嵌入。为了解决误报问题，在对奇异值进行分解之前，先通过Arnold变换和FRFT对放大后的水印进行两次加密，由于生成了更多的密钥，因此增强了算法的安全性。多参数粒子群优化（MP-PSO）用于获得最佳嵌入因子，以实现隐形性和鲁棒性之间的平衡。仿真结果和对比实验表明，该算法在满足安全性，可靠性和不可见性的前提下表现出较高的鲁棒性，特别是对于旋转，裁剪，平移等几何攻击。