Optimal linear detector for spread spectrum based multidimensional signal watermarking

This paper presents a new efficient spread spectrum (SS) based watermarking technique for multidimensional signals. In this method, the Karhunen Loeve transform (KLT) is used to completely decorrelate the components of the cover signal and obtain the maximum energy compaction. In order to improve the robustness, the same secret message is embedded into all components and linear fusion is used to exploit the collaboration among the local correlation detectors. Based on a theoretic analysis, the condition for perfect reconstruction of the KLT without the original signal is established. The performance of the proposed scheme is considered for both average and optimal detector and a closed-form expression of the optimal weighting coefficients to minimize the error probability is then derived. Experimental results are provided in the context of color image watermarking, with and without additive Gaussian noise attack.