# An Adaptive and Secure Holographic Image Watermarking Scheme
## 1 Introduction
The encrypted kinoform was generated by a non-cascade phase retrieval algorithm. The main shortcomings of this method are that the quality of the reconstruction of the mark kinoform is decreased and the phase retrieval algorithm has a high complexity. In previous work [13], the phase-shifting interferometry-based CGH was inserted into the contourlet-transformed host image, and the embedding parameter is optimized by the use of particle swarm optimization. However, the computational complexity of this optimal scheme is high. In the above-mentioned methods, the watermarks are gray-level holograms. Due the advantage of being stored, transferred and replicated [14], the binary hologram is superimposed on the low-frequency wavelet coefficients of the original image using quantization index modulation [15]. But the parameter of this watermarking method is determined experimentally. Additionally, the watermarking method with an adaptive texturized algorithm is also developed to protect digital hologram recently [16]. Though DWT has been applied widely in watermarking and image processing [8] due to its good properties such as multiscale and time frequency localization, it cannot capture the directional information of images effectively. This weakness is overcome by contourlet transform (CT) [17]. However, the efficiency of contourlets in representing smooth contours of an image is decreased because of some waste components [7; 8]. This drawback is settled by use of sharp frequency localized contourlet transform (SFLCT) [18]. In addition, SVD alone is not preferred owing to the large computation cost [4]. Compared with SVD, Schur decomposition has the advantage of lower computational complexity because it is a major intermediate step in SVD [19; 20]. Therefore, in this study, the advantages of SFLCT and Schur decomposition are considered to enhance the performance of image watermarking. Moreover, to gain both imperceptibility and robustness in terms of the watermarking requirements, the entropy and edge entropy are utilized to choose the suitable positions to embed the watermark. Furthermore, the security risks of the traditional holographic watermarking methods are increased because of the small key space of hologram watermark. Hence, to enhance the security of watermarking system, the chaotic maps that are extreme sensitive to initial conditions are adopted to develop a new encrypted computer-generated hologram algorithm in this work. The hologram fabricated by this algorithm has a huge key space. In this paper, a secure adaptive holographic watermarking scheme is presented. To enhance the security of the watermarking system, a novel encrypted binary CGH method based on sine logistic modulation map (SLMM) and logistic map is designed to fabricate a hologram watermark. The mark CGH is superposed on the original image which is transformed by SFLCT and Schur decomposition. The entropy and the edge entropy are employed to choose the positions which are suitable for embedding to achieve a high imperceptibility without losing the robustness in the embedding procedure. The watermark can be extracted without the host image during the watermark extraction process. Compared with other published schemes, the proposed method offers better performance better performance in both imperceptibility and robustness. Experiments exhibit that the proposed watermarking method, in addition to high security and transparency, has good robustness against different kinds of attack.