Joint robust watermarking and compression using variable-rate scalar quantization

In this paper we are interested in the design of joint watermarking and compression (JWC) systems to obtain an efficient tradeoff among the embedding rate, composite rate, encoding distortion, and robustness. Using variable-rate scalar quantization (VRSQ) for watermarking and compression, we first present an optimum binary JWC encoding algorithm to maximize the robustness of the systems in the presence of additive Gaussian attacks under constraints on both of the composite rate and encoding distortion, and then show the convergence of the algorithm. It is further demonstrated by simulation that in the distortion-to-noise ratio (DNR) region of practical interest, optimal JWC systems designed using VRSQ achieve about 0:3-dB DNR gain over optimal JWC systems using fixed-rate scalar quantization (FRSQ) for an independent and identically distributed (i.i.d.) Gaussian source. As an application of JWC design using VRSQ to image watermarking and compression, a joint odd-even watermarking (OEW) and JPEG compression scheme is developed and demonstrated to achieve better embedding performance than the JPEG-compatible differential energy watermarking (DEW) scheme and the differential quantization watermarking (DQW) scheme developed in the recent literature.