Optimal watermark power and host samples allocation under random gain attack

This paper proposes an optimal algorithm that minimizes watermark power (hence embedding distortion) subject to meeting the strict data hiding rate constraint in presence of joint additive noise and random gain attack. The proposed algorithm approaches such problem using convex optimization framework and gets the solution for watermark power and host sample allocation. This offers an optimality in terms of embedding distortion-robustness-data hiding capacity with polynomial computation complexity. Simulation carried over convolution coded integer wavelet coefficients on compressed host image show that ~ 4.5 to ~ 3 times less normalized watermark power is required in the proposed system. This leads to an improvement of ~ 10 dB in document- to-watermark ratio over direct embedding on entropy coded data. Simulation results also show that an improvement in bit error rate of 10^-2 is achieved over fixed memoryless attack channel.