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We treat a digital watermarking in digital still image based on discrete wavelet transform (DWT). For copyright protection, ID is embedded in DWT domain by using key sequence. For security, it is desirable to be hard to counterfeit the key and ID. In this work, we propose a watermarking method with new key sequence in the DWT domain. By using the proposed method, it is difficult to counterfeit the key and ID. Additionally, we show how to design the key sequence so that the robustness of the watermark is strong. Finally, we show the robustness against jpeg attack on the proposed watermarking method by computer simulation.

The problem of minimizing an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints for three-dimensional (3-D) separable-denominator digital filters is formulated. The constrained optimization problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, an efficient quasi-Newton algorithm is applied with closed-form formula for gradient evaluation to solve the unconstrained optimization problem. The optimal filter structure is then constructed by employing the resulting coordinate transformation matrix that minimizes the L2-sensitivity measure subject to the scaling constraints. A numerical example is presented to illustrate the utility of the proposed technique.