A new look at ML step-size estimation for Scalar Costa scheme data hiding

Watermarking schemes based on the Dirty Paper Coding (DPC) paradigm have been shown to achieve much higher rates than classical Spread-Spectrum methods. However, in practice, the latter continue to be used due to their higher security and robustness. In fact, the most prevalent DPC method, the so-called Scalar Costa Scheme (SCS), is prone to non-additive attacks, such as a simple gain which produces a desynchronization between the embedding and decoding codebooks thus severely affecting performance. Although some gain-robust modifications to the basic SCS exist, all have serious drawbacks. One alternative, which was somehow abandoned for its complexity, is to estimate the gain at the decoder, with the advantage of preserving the simplicity of SCS. In this paper we take a new look at the estimation problem and propose an affordable algorithm to perform Maximum Likelihood estimation of the channel gain, that is able to restore the original SCS performance. We also show and experimentally illustrate how our scheme can be effectively adapted to watermark decoding in filtered images.