Statistical analysis of a watermarking system based on Bernoulli chaotic sequences

摘要

The paper deals with the statistical analysis of the behaviour of a blind copyright protection watermarking system based on chaotic watermark signals generated by n-way Bernoulli shift maps. The analysis involves theoretical evaluation of the system detection reliability, when a correlator detector is used. The effect of distortions (lowpass filtering, noise corruption of the watermarked data) on the detection reliability is also theoretically investigated. The system is modelled in a communication framework considering the signal as interference and converting the addressed problem to the detection of the underlying watermark signal. The aim of the paper is two-fold: (i) to introduce the n-way Bernoulli shift generated chaotic watermarks and theoretically contemplate their properties with respect to the detection reliability and (ii) to theoretically establish their potential superiority against the widely used (pseudo-)random water- marks. An important property of Bernoulli watermarks is their controllable spectral/correlation properties that renders them ideal for a variety of applications. Bernoulli watermarks can be generated with lowpass spectral properties to withstand lowpass attacks. When no distortions are to be inflicted, white spectrum Bernoulli watermarks can be generated so that their performance converges to that of the random watermarks. Experimental verification of the theoretical analysis results has been performed as well.