طرح نهان نگاری کاربردی براساس طیف گسترده و تئوری بازی

In this paper, we consider the implementation of robust watermarking scheme for non-i.i.d. Gaussian signals and distortion based on perceptual metrics. We consider this problem as a communication problem and formulated it as a game between an attacker and an embedder in order to establish its theoretical performance. We first show that known parallel Gaussian channels technique does not lead to valid practical implementation, and then propose a new scheme based on Wide Spread Spectrum and Side Information. Theoretical performances of this scheme are established and shown to be very close to the upper bound on capacity defined by Parallel Gaussian channels. Practical implementation of this scheme is then presented and influence of the different parameters on performance is discussed. Finally, experimental results for image watermarking are presented and validate the proposed scheme.

A lot of effort has been dedicated over the last years for designing practical watermarking systems. The approaches were often viewing the media content as noise from the watermark detection perspective, hence regarding watermarking as a form of wide spread spectrum communication (WSS) with various forms of distortion measures (MSE or weighted MSE) and of channel characterizations [13], [16] and [28]. The authors in [6] suggest to take into account the perceptual properties of the content and to embed in perceptually significant frequency components. Other approaches based on WSS and exploiting the perceptual sensitivity of the host data can also be found in [24], [26] and [30]. However these techniques are based on empirical assumptions. Attacks have often been modeled as the addition of White Gaussian noise (AWGN) [21] and [27], and more recently as linear filtering plus white or colored additive noise [19] and [29]. It has been shown in [1] and [7] that expressing the problem of watermarking as a problem of communication with side information leads to optimal performances. Costa [5] has indeed shown that in the context of attacks modeled by AWGN, the capacity is not dependent on the cover signal. However the solution proposed, known as the Ideal Costa Scheme (ICS), requires very large codebooks, hence is not realistic. Different approaches have then been proposed to reach performances of Costa's scheme using structured codebooks; Scalar Costa Scheme (SCS) [10], syndrome based coding [2] or more recently trellis with multiple paths [18]. Dithered quantization techniques [1] and [25] may also be seen as techniques exploiting side information. Most of these schemes are defined for i.i.d. signals which is not a valid assumption for usual considered signals. Techniques based on parallel-Gaussian channels [4] and [20] have then been proposed to deal with such non-i.i.d. Gaussian signals. However practical implementation of Parallel-Gaussian necessitates to know the original signal [17] and does not lead to a valid implementation (see discussion in Section 2). This paper deals with the robust data hiding problem, assuming a blind (the extraction system has no knowledge of the host signal) and symmetric (same private key for embedding and extraction) system. In this paper we consider this problem as a communication problem: one seeks the maximum hiding capacity (or rate of reliable transmission) over any hiding and attack strategies. The rate obviously depends on the perceptual distortion levels considered admissible and on the watermark channel (or attack scenarios) characterization. We especially present a technique based on Wide Spread Spectrum and Side Information facing Scaling and Additive White Gaussian Noise (SAWGN) optimized by considering Game Theory formalism in order to define performance limits. Practical implementation as well as efficiency of the proposed technique are further presented. This paper is organized as follows. In Section 2, general consideration about watermarking of non-i.i.d. signals is first presented as well as limitation of the previously proposed techniques. In Section 3, we then present an optimized watermarking scheme based on Wide Spread Spectrum and Side Information and discuss about its practical implementation. In Section 4, experimental results are shown for image watermarking. Finally Section 5 concludes this work.

In this paper we have studied the implementation of a practical watermarking scheme for non-i.i.d. Gaussian signals and perceptual metrics for distortion. We have first shown that theoretical approach based on parallel Gaussian channels should not be perform with embedding/extraction on separate channels. We then reformulated the watermarking problem considering global embedding/extraction based on WSS and Side Information. Theoretical performances of this scheme has been established by considering a game between an attacker and the embedder for SAWGN attacks. This watermarking scheme leads to a practical implementation of Side Information scheme with performance very close to the upper-bound defined by parallel Gaussian Channels. Application to image watermarking has been validated by successfully resisting to all non geometrical Stirmark attacks.