Blind Image Watermark Decoder in UDTCWT Domain Using Weibull Mixtures-Based Vector HMT

Abstract

As one promising solution, digital watermarking has been proposed to resolve image copyright protection and content authentication, and has been applied successfully in many fields. Owing to their excellent description capability and invariance property, statistical models have become a popular tool for the image watermarking resulting in favorable trade-offs among imperceptibility, robustness and data payload. By modeling the robust undecimated dual tree complex Wavelet transform (UDTCWT) coefficient magnitudes with the Weibull mixtures based vector hidden Markov trees (HMT) and employing maximum likelihood (ML) test criterion, we propose a new image watermarking approach in UDTCWT domain in this paper. Our image watermarking approach consists of two parts, namely, embedding and extracting. In the embedding process, we compute the robust UDTCWT coefficient magnitudes with UDTCWT domain real/imaginary parts, and insert the digital watermark into the significant UDTCWT coefficient magnitude subband. In the extracting phase, robust UDTCWT coefficient magnitudes are firstly modeled by employing the Weibull mixture-based vector HMT, where the statistical properties of UDTCWT magnitudes are captured accurately. Then the expectation/conditional maximization (ECM) approach is introduced to estimate the statistical model parameters. Finally, an image watermark decoder for multiplicative watermarking is developed using the Weibull mixtures based vector HMT and ML test. The experiments show that the proposed method not only improves the imperceptibility, but also increases the robustness performance and outperforms state-of-the-art methods on a set of standard test images.