Abstract
This article investigates efficient blind watermark decoding approaches for hidden messages embedded into host images, within the framework of additive spread spectrum (SS) embedding based for data hiding. We study SS embedding in both the discrete cosine transform and the discrete Fourier transform (DFT) domains. The contributions of this article are multiple-fold: first, we show that the conventional SS scheme could not be applied directly into the magnitudes of the DFT, and thus we present a modified SS scheme and the optimal maximum likelihood (ML) decoder based on the Weibull distribution is derived. Secondly, we investigate the improved spread spectrum (ISS) embedding, an improved technique of the traditional additive SS, and propose the modified ISS scheme for information hiding in the magnitudes of the DFT coefficients and the optimal ML decoders for ISS embedding are derived. We also provide thorough theoretical error probability analysis for the aforementioned decoders. Thirdly, sub-optimal decoders, including local optimum decoder (LOD), generalized maximum likelihood (GML) decoder, and linear minimum mean square error (LMMSE) decoder, are investigated to reduce the required prior information at the receiver side, and their theoretical decoding performances are derived. Based on decoding performances and the required prior information for decoding, we discuss the preferred host domain and the preferred decoder for additive SS-based data hiding under different situations. Extensive simulations are conducted to illustrate the decoding performances of the presented decoders.
Highlights
The growing use of Internet has enabled the users to access, share, manipulate, and distribute the digital media data, and digital media has profoundly changed our daily life during the past decade
Derive the maximum likelihood (ML) and generalized maximum likelihood (GML) decoders for spread spectrum (SS) and improved spread spectrum (ISS) in the discrete Fourier transform (DFT) magnitude domain; Derive the ML decoder for ISS embedding in the discrete cosine transform (DCT) domain
For information embedding in the DCT domain, for each 8 × 8 block of the image, the DCT coefficients are calculated and all coefficients except the dc one are used as the host signal to convey the hidden information, 63 coefficients are used for conveying of one bit of information
Summary
The growing use of Internet has enabled the users to access, share, manipulate, and distribute the digital media data, and digital media has profoundly changed our daily life during the past decade. Even though ML criterion has been used for both watermark detection and watermark decoding, it is derived differently and has different meanings (i.e., the ML watermark decoder is a Bayesian approach to minimizes the probability of bit error when assuming the equal prior probability of the bit information and assuming the threshold to be 1; while for watermark detection, the ML solution is the likelihood ratio test (LRT) detector based on the Neyman-Pearson theorem, where the LRT exploits the probability of false alarm to set the detection threshold). Our main purpose is to provide a rigorous watermark decoding framework for data hiding using spread spectrum embedding in the DCT domain and the DFT magnitude domain.
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