Analysis of pilot-based synchronization algorithms for watermarking of still images

In this paper we present an analytical approach to pilot-based synchronization algorithms for data hiding in still images. A representative algorithm belonging to the family of those exploiting a regular structure in the spreading sequence is chosen for study. We improve it by proposing the use of the Levenberg–Marquardt’s method for nonlinear least-squares estimation, and show how an estimate of the geometrical transformation parameters can be obtained. A statistical model for the estimation error in the parameters is derived and theoretically justified. This allows to quantify the resolution of the algorithm for a certain watermark structure. Moreover, the increase in the bit error probability of the hidden information for a given transformation and interpolation scheme is theoretically analyzed and quantified. Finally, we provide experimental results that support our analysis. r 2002 Elsevier Science B.V. All rights reserved.