Optimizing Additive Approximations of Non-additive Distortion Functions

The progress in steganography is hampered by a gap between non-additive distortion functions, which capture well complex dependencies in natural images, and their additive counterparts, which are efficient for data embedding. This paper proposes a theoretically justified method to approximate the former by the latter. The proposed method, called Backpack (for BACKPropagable AttaCK), combines new results in the approximation of gradients of discrete distributions with a gradient of implicit functions in order to derive a gradient w.r.t. the distortion of each JPEG coefficient. Backpack combined with the min max iterative protocol leads to a very secure steganographic algorithm. For example, the error rate of XuNet on 512 X 512 JPEG images, compressed with quality factor 100 and a payload of 0.4 bits per non-zero AC coefficient is 37.3% with Backpack, compared to a 26.5% error rate using ADV-EMB with minmax (considered state of the art in this work) and a 16.9% error rate with J-UNIWARD.