An analysis of quantization influence on optimal detection of multiplicative watermark

Analysis of quantization effects on watermarked coefficients and watermark is considered. A criterion for selection of coefficients suitable for watermarking in the presence of quantization is derived. The effects of quantization are further analyzed in terms of the probability of detectable watermark and the probability of zero-quantized watermarked coefficients. This analysis is used to define an image watermarking procedure that provides robustness to an arbitrary JPEG compression/quantization degree. Theoretical results are illustrated by examples.