Steganographic capacity estimation for the statistical restoration framework

In this paper we attempt to quantify the "active" steganographic capacity - the maximum rate at which data can be hidden, and correctly decoded, in a multimedia cover subject to noise/attack (hence - active), perceptual distortion criteria, and statistical steganalysis. Though work has been done in studying the capacity of data hiding as well as the rate of perfectly secure data hiding in noiseless channels, only very recently have all the constraints been considered together. In this work, we seek to provide practical estimates of steganographic capacity in natural images, undergoing realistic attacks, and using data hiding methods available today. We focus here on the capacity of an image data hiding channel characterized by the use of statistical restoration to satisfy the constraint of perfect security (under an i.i.d. assumption), as well as JPEG and JPEG-2000 attacks. Specifically we provide experimental results of the statistically secure hiding capacity on a set of several hundred images for hiding in a pre-selected band of frequencies, using the discrete cosine and wavelet transforms, where a perturbation of the quantized transform domain terms by ±1 using the quantization index modulation scheme, is considered to be perceptually transparent. Statistical security is with respect to the matching of marginal statistics of the quantized transform domain terms.