Optimal Detector for Multiplicative Watermarks Embedded in the DFT Domain of Non-White Signals
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Optimal Detector for Multiplicative Watermarks Embedded in the DFT Domain of Non-White Signals Vassilios Solachidis Department of Informatics, University of Thessaloniki, 54124 Thessaloniki, Greece Email: [email protected]
Ioannis Pitas Department of Informatics, University of Thessaloniki, 54124 Thessaloniki, Greece Email: [email protected] Received 28 September 2003; Revised 10 June 2004 This paper deals with the statistical analysis of the behavior of a blind robust watermarking system based on pseudorandom signals embedded in the magnitude of the Fourier transform of the host data. The host data that the watermark is embedded into is one-dimensional and non-white, following a specific probability model. The analysis performed involves theoretical evaluation of the statistics of the Fourier coefficients and the design of an optimal detector for multiplicative watermark embedding. Finally, experimental results are presented in order to show the performance of the proposed detector versus that of the correlator detector. Keywords and phrases: Fourier transform, watermarking, detector, signal processing.
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INTRODUCTION
The risk of illegal copying, reproduction, and distribution of copyrighted multimedia material is becoming more threatening with the all-digital evolving solutions adopted by content providers, system designers, and users. Thus, copyright watermark protection of digital data is an essential requirement for multimedia distribution. Robust watermarks can offer a copyright protection mechanism for digital media. The watermark is a signal that contains information about the copyright owner and it is embedded permanently in the multimedia data. It introduces imperceptible content changes that can be detected by a detection program. Robustness is a very important property of the watermarking scheme. The watermarks must be robust to distortions, such as those caused by image processing algorithms (in the case of image watermarks). Image processing modifies not only the image but also may modify the watermark as well. Thus, the watermark may become undetectable after intentional or unintentional image processing attacks. The watermark must also be imperceptible. The watermark alterations should not decrease the perceptual media quality. A general watermarking framework for copyright protection has been presented in [1, 2] and it describes all these issues in detail.
Watermarking methods can be distinguished in two major classes, according to the embedding/detection domain. In the first class, the embedding is performed directly in the spatial domain [3, 4, 5]. The second class is referred to as transform domain techniques. In these methods, the watermark is embedded in a transform domain, attempting to exploit the transform properties mainly for watermark imperceptibility and robustness. The watermark can be embedded in the DCT [6, 7, 8, 9], discrete Fourier transform (DFT) [10, 11], Fourier-Mellin [12, 13], DWT [7, 14, 15, 16, 17, 18] or fractal-based coding domains [19, 20]. Many approaches ad
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