Secure Steganography: Statistical Restoration in the Transform Domain with Best Integer Perturbations to Pixel Values

We consider the problem of active steganography, wherein the goal is to survive benign attacks in addition to maintaining statistical and perceptual transparency. The stego image can be “advertised” in uncompressed format, but they can survive JPEG compression upto a certain design quality factor while still resisting statistical steganalysis. The data is hidden in the discrete cosine transform (DCT) coefficients using the statistical restoration framework: a fraction of the coefficients are used for hiding and the rest are used for restoring the statistics. In order to advertise the images in uncompressed format, we must restore the unquantized or continuous statistics. This paper extends the statistical restoration framework so as to make only integer perturbations to the pixel values while modifying the transform coefficients, thus matching their histogram computed using very small bin-width. We present numerical results confirming the applicability of the presented technique.