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A novel adaptive secure holographic image watermarking method in the sharp frequency localized contourlet transform (SFLCT) domain is presented. Based upon the sine logistic modulation map and the logistic map, we develop an encrypted binary computer-generated hologram technique to fabricate a hologram of a watermark first. Owing to the enormous key space of the encrypted hologram, the security of the image watermarking system is increased. Then the hologram watermark is embedded into the SFLCT coefficients with Schur decomposition. To obtain better imperceptibility and robustness, the entropy and the edge entropy are utilized to select the suitable watermark embedding positions adaptively. Compared with other watermarking schemes, the suggested method provides a better performance with respect to both imperceptibility and robustness. Experiments show that our watermarking scheme for images is not only is secure and invisible, but also has a stronger robustness against different kinds of attack.