Hidden information detection using decision theory and quantized samples: Methodology, difficulties and results

• Quantization impact on design/performance of optimal hidden data test is studied.
• For small noise to quantization ratio, the optimal LR test performance is given.
• Simplification for large noise to quantization ratio is also presented.
• For unknown medium analysis, a GLR test is proposed and its performance is given.
• Impact of medium parameters on hidden data detectability are given for the first time.

This paper studies the detection of Least Significant Bits (LSB) steganography in digital media by using hypothesis testing theory. The main goal is threefold: first, it is aimed to design a test whose statistical properties are known, this especially allows the guaranteeing of a false alarm probability. Second, the quantization of samples is studied throughout this paper. Lastly, the use of a linear parametric model of samples is used to estimate unknown parameters and design a test which can be used when no information on cover medium is available. To this end, the steganalysis problem is cast within the framework of hypothesis testing theory and digital media are considered as quantized signals. In a theoretical context where media parameters are assumed to be known, the Likelihood Ratio Test (LRT) is presented. Its statistical performances are analytically established; this highlights the impact of quantization on the most powerful steganalyzer. In a practical situation, when image parameters are unknown, a Generalized LRT (GLRT) is proposed based on a local linear parametric model of samples. The use of such model allows us to establish GLRT statistical properties in order to guarantee a prescribed false-alarm probability. Focusing on digital images, it is shown that the well-known WS (Weighted-Stego) is close to the proposed GLRT using a specific model of cover image. Finally, numerical results on natural images show the relevance of theoretical findings.

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