Locally Optimal Detection of Image Watermarks in the Wavelet Domain Using Bessel K Form Distribution

Abstract

A uniformly most powerful watermark detector, which applies the Bessel K form (BKF) probability density function to model the noise distribution was proposed by Bian and Liang. In this paper, we derive a locally optimum (LO) detector using the same noise model. Since the literature lacks thorough discussion on the performance of the BKF-LO nonlinearities, the performance of the proposed detector is discussed in detail. First, we prove that the test statistic of the proposed detector is asymptotically Gaussian and evaluate the actual performance of the proposed detector using the receiver operating characteristic (ROC). Then, the large sample performance of the proposed detector is evaluated using asymptotic relative efficiency (ARE) and "maximum ARE." The experimental results show that the proposed detector has a good performance with or without attacks in terms of its ROC curves, particularly when the watermark is weak. Therefore, the proposed method is suitable for wavelet domain watermark detection, particularly when the watermark is weak.