Performance analysis and improvement of dither modulation under the composite attacks

The first goal of this article is to analyze the performance of dither modulation (DM) against the composite attacks including valumetric scaling, additive noise and constant change. The analyzes are developed under the assumptions that the host vector and noise vector are mutually independent and both of them have independently and identically distributed components. We derive the general expressions of the probability density functions of several concerned signals and the decoding error probability. The specific theoretical results are provided for the case of generalized Gaussian host and noise. Based on the analyzes, the performance of DM is predicted for different scenarios with a high degree of accuracy and evaluated for different distribution models of host and noise signals. Numerical simulations confirm the validity of the given theoretical analyzes. Then, we address to improve the robustness of DM against valumetric scaling plus constant change. The normalized dither modulation (NDM) is presented, which works by constructing a gain-invariant vector with zero mean for quantization. Performance analysis shows that NDM is theoretically invariant to valumetric scaling and constant change and achieves similar performance to DM in other aspects. The performance of NDM is further improved by weighting the quantization errors. Experiments on real images also show the advantage of NDM over DM subject to amplitude scaling and constant change.