Embedding Distortion Modeling for Non-orthonormal Wavelet based Watermarking Schemes

In this paper a universal embedding distortion model for wavelet based watermarking is presented. The present work extends our previous work on modelling embedding distortion for watermarking algorithms that use orthonormal wavelet kernels to non-orthonormal wavelet kernels, such as biorthogonal wavelets. By using a common framework for major wavelet based watermarking algorithms and the Parseval's energy conservation theorem for orthonormal transforms, we propose that the distortion performance, measured using the mean square error (MSE), is proportional to the sum of energy of wavelet coefficients to be modified by watermark embedding. The extension of the model to non-orthonormal wavelet kernel is obtained by rescaling the sum of energy of wavelet coefficients to be modified by watermark embedding using a weighting parameter that follows the energy conservation theorems in wavelet frames. The proposed model is useful to find optimum input parameters, such as, the wavelet kernel, coefficient selections and subband choices, for a given wavelet based watermarking algorithm.