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Mathematical Problems in Engineering
Volume 2016, Article ID 4065215, 18 pages
Research Article

NSCT Domain Additive Watermark Detection Using RAO Hypothesis Test and Cauchy Distribution

1School of Electrical Information Engineering, Northeast Petroleum University, Daqing 163318, China
2College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China

Received 13 September 2015; Revised 1 February 2016; Accepted 15 February 2016

Academic Editor: Erik Cuevas

Copyright © 2016 Hongbo Bi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We presented a RAO hypothesis detector by modeling Cauchy distribution for the Nonsubsampled Contourlet Transform (NSCT) subband coefficients in the field of additive spread spectrum image watermarking. Firstly, the NSCT subband coefficients were modeled following the Cauchy distributions, and the Fit of Goodness shows that Cauchy distribution fits the NSCT subband coefficients more accurately than the Generalized Gaussian Distribution (GGD) commonly used. Secondly, a blind RAO test watermark detector was derived in the NSCT domain, which does not need the knowledge of embedding strength at the receiving end. Finally, compared to the other three state-of-art detectors, the robustness of the proposed watermarking scheme was evaluated when the watermarked images were attacked by JPEG compression, random noise, low pass filtering, and median filtering. Experimental results show that, compared with the other three detectors, the proposed RAO detector guarantees the lower probability of miss under the given probability of false alarm.