Performance Analysis of Scalar DC-QIM Forwatermark Detection

Quantization-based schemes, such as scalar DC-QIM, have demonstrated performance merits for data-hiding problem, which is mainly a transmission problem. However, a number of applications are stated in terms of watermark detection problem (also named one-bit watermarking), and this situation has been seldom addressed in the literature for quantization-based techniques. In this context, we carry out a complete performance analysis of uniform quantizers-based schemes with distortion compensation (DC) under additive white Gaussian noise. Implementing an exact Neyman-Pearson test and using large deviation theory, performances are evaluated according to receiver operating characteristic (ROC) and probability of error. Optimal DC´s regarding to ROC performances are derived. It is pointed out that false-alarm and miss detection capabilities are jointly optimized by the same DC value. Then, performances are compared with raw quantized-schemes (i.e. without DC) and spread-spectrum (SS) watermarking. It is shown that DC-QIM always outperforms QIM and SS for detection task. The gain provided by the DC reaches several orders of magnitude for cases of interest, that is for low watermark-to-noise regimes. A short comparison is also provided with respect to the corresponding transmission problem, thus evaluating the loss in performance due to the detection