Faster Design of Robust Binary Joint Watermarking and Scalar Quantization under Additive Gaussian Attacks

Abstract

This thesis investigates the problem of optimal design of binary joint watermarking and scalar quantization (JWSQ) systems that are robust under additive Gaussian attacks. A binary JWSQ system consists of two quantizers with disjoint codebooks. The joint quantization and embedding are performed by choosing the quantizer corresponding to the embedded message. The optimal JWSQ design for both fixed-rate and variable-rate cases was considered in the past, but the solution approaches exhibited high computational complexity.

In this thesis, we propose faster binary JWSQ design algorithms for both the fixed-rate and variable-rate scenarios. We achieve the speed up by mapping the corresponding optimization problem to a minimum weight path problem in a certain weighted directed acyclic graph (with a constraint on the length of the path in the fixed-rate case). For this mapping to be possible we discretize the quantizer space and use an approximation for the probability of decoding error. The proposed solution algorithms have $O(LN^3)$ and $O(N^4)$ time complexity in the two cases respectively, where $N$ is the size of discretized source alphabet, and in the fixed-rate scenario $L$ is the number of cells in each quantizer.

The effectiveness of the proposed designs is assessed through extensive experiments on a Gaussian source. Our results show that our algorithms are able to achieve performance very close to the prior existing schemes, but only at a small fraction of their running time.