A new detector for contourlet domain multiplicative image watermarking using Bessel K form distribution

•Studying the compatibility between contourlet coefficients and BKF distribution.•Designing an optimal LRT detector for multiplicative contourlet domain watermarking.•Calculating the ROC and analyzing the detector performance analytically.

This paper proposes a novel multiplicative contourlet domain watermark detector. We use contourlet transform since this transform represents image edges sparsely and this makes it suitable for human visual system. Watermark detection can be formulated as a binary statistical decision problem, so, its performance is dependent on the accuracy of statistical modeling. Studying the statistical properties of contourlet coefficients, we demonstrate the high efficiency of Bessel K form (BKF) distribution to model these coefficients. Consequently, we design an optimal detector for multiplicative watermarking based on using the Maximum Likelihood (ML) decision rule and BKF distribution. Also, we derive its receiver operating characteristics analytically. Experimental results demonstrate the high efficiency of the proposed scheme under different types of attacks. Finally, we compare our proposed detector with other related detectors experimentally using Monte Carlo simulations and verify the performance improvement in utilizing the new strategy.