Blind optimum detector for robust image watermarking in nonsubsampled shearlet Domain

In this paper, we propose a blind robust image watermarking approach in the nonsubsampled Shearlet domain using Bessel K Form (BKF) modeling. Nonsubsampled shearlet transform (NSST) is an effective multi-scale and multi-direction analysis method, it not only can exactly compute the shearlet coefficients based on a multiresolution analysis, but also can provide nearly optimal approximation for a piecewise smooth function. In order to achieve more robustness and imperceptibility, watermark information is embedded into the most significant NSST directional subband with the highest energy, by simply modifying the NSST coefficient amplitude according to the watermark data. By modeling the NSST coefficients with BKF probability density function, the distribution of watermarked noisy coefficients is analytically calculated. The tradeoff between the imperceptibility and robustness of watermark data is solved in a novel fashion. At the receiver, based on the Maximum Likelihood (ML) decision rule, a blind statistical watermark detector is proposed. Experimental results on test images demonstrate that the proposed approach can provide better imperceptibility and robustness against various attacks, such as additive white Gaussian noise, salt & pepper noise, median filtering, JPEG compression, rotation, and scaling, in comparison with the recently proposed techniques.