Statistical detection of digital holographic watermarking system

In this paper, we examine the statistical properties of the holographic watermarking system [C.J. Cheng, L.C. Lin, W.T. Dai, Opt. Commun. 248 (2005) 105] and facilitate a systematic way to determine an optimal threshold of the correlation signal for detecting the authorized mark pattern. The holographic watermarking system constructs a digital holographic watermark using modified Mach–Zehnder interferometric architecture, and the correlation signal is obtained using an optical VanderLugt 4-f correlator to identify the authorized mark in the watermarked image. To obtain the best detection performance, we use statistical modeling of the entire holographic watermarking system. Accordingly, we derive correlation signal statistics and hypothesis testing to obtain an optimal threshold for the watermark detector that minimizes the detection error. The theoretical result of this paper allows us to easily determine an optimal threshold and evaluate the robustness of the watermark detector. The robustness of the proposed optimal detector is evaluated using detection error, and detection performance is demonstrated by simulation experiments.