Second-order steganographic method based on adaptive reference matrix

A second-order steganographic method (SOS) based on pixel pair matching and modification direction exploiting (MDE) is proposed in this study. In SOS, each cover pixel pair is used to conceal two secret digits in a B-ary notational system. Therefore the maximum embedding rate (ER) is up to log₂B bit per pixel (bpp). It is different from the previous MDE-based methods in which only one secret digit in base B can be embedded into each cover pixel pair and the maximum ER is 1/2 log₂B bpp. The experimental results demonstrate the improvements to the proposed method in terms of capacity, efficiency and detection rate compared to recent MDE-based methods. Take B = 3 as an example. The ER is 1.585 bpp and the corresponding average peak-signal-to-noise-rate is 49.89 dB, demonstrating the best image quality with the same embedding rate compared to recent MDE-based methods.