Efficient blind decoders for additive spread spectrum embedding based data hiding

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.

Covert communications through mobile voice channels

“…The key signal is a pseudorandom binary sequence where s i ∈ {− 1, 1}, and, finally, α represents the embedding strength. To improve the performance and have a host‐rejection approach at the receiver side which decreases the error probability, the improved spread spectrum (ISS) method can be used as follows [13] where k is derived by minimising the probability of error. The distortion for this structure could be computed as where R x is the autocorrelation matrix of the host signal.…”

“…In doing so, two simple suboptimum detectors based on LOD and GML are proposed. Noting that due to imperceptibly concerns the value of embedding strength is small, the LOD decoder could be derived by using the first order Taylor expansion of z ML ( α ) around zero [13] Discarding the higher order terms and carrying out some straight forward mathematical operations, we have The derived LOD detector is independent of α , but it still requires the value of θ . Thus, in this suboptimal decoder, the shape parameter should be known or estimated at the receiver side.…”

“…In some cases, especially when θ varies frequently, this parameter could not be estimated with sufficient precision. To overcome with this drawback, we propose a new decoder based on GML concepts [13].…”