Less is More: Reversible Steganography with Uncertainty-Aware Predictive Analytics

features for making predictions [31]–[33]. A recent study has demonstrated that a convolutional neural network (CNN) with multi-scale receptive field can extract multi-scale image features and hence has better performance than that of traditional predictors, which use relatively limited contextual information [34]. Another study has established a connection between low-level computer vision and intensity prediction [35], and adopts the memory-persistent network (MemNet) originally proposed for super-resolution imaging and image denoising [36]. Prediction accuracy is content-dependent: in general, it is high for smooth regions and low for rough regions. A potential way to improve prediction accuracy is to adaptively filter out some unpredictable regions. This can be done by formulating a function that analyses pixel correlations and estimates local pattern complexity [37]–[39]. However, the identified unpredictable regions are bounded within the confines of general principles (e.g. smoothness prior) laid out by handcrafted statistical analytics. In addition, we argue that this kind of prescriptive method appears to fall short of capturing true uncertainty (or predictability), defined as the degree to which a correct prediction can be made by a given predictor. From our perspective, uncertainty is not only associated with the image content but also with the predictor used. We thus must analyse for which types of patterns a given predictor has the highest probability of making accurate predictions. Learningbased analytics can learn to follow some of the basic principles and, at the same time, adapt to a specific predictor because it TABLE I LIST OF VARIABLES AND OPERATIONS var. & op. definition x cover image x′ stego image x̄ processed image xC context pixels xQ query pixels x̃Q adaptively selected query pixels y predicted pixels ε residuals m message v overflow-status register ω payload φ uncertainty map α stego-channel parameter netφ neural network for uncertainty estimation nety neural network for intensity prediction scale⇓ downscaling of possibly overflowing pixels scale⇑ upscaling of possibly overflowing pixels split context-query splitting merge context-query merger select adaptive selection of predictable pixels replace replacement of predictable pixels modulate residual modulation (payload embedding) de-modulate residual de-modulation (payload extraction) concat concatenation of bit-streams de-concat de-concatenation of bit-streams does not have a preconceived notion. The concept of self-awareness, albeit illusive and indefinite, can be understood as the ability to know one’s own strengths and limitations. While there is no indication that contemporary artificial intelligence is anywhere close to engendering selfawareness, a rudimentary kind of self-aware machine should be able to realise whether or not it can handle a given query: the machine knows what it knows and does not know. It thus could be given a reject option and be allowed to abstain from making a prediction when there is a large amount of uncertainty [40]–[44]. Following the ‘less is more’ philosophy, our objective is to build an uncertainty-aware predictive module by endowing it with an option to exercise abstention and thereby improve prediction accuracy. In this paper, we study uncertainty-aware predictive analytics for reversible steganography. In summary, our aim is to create a robust and reliable predictive module with a reject option. To this end, we introduce both supervised and unsupervised learning for training uncertainty analysers by which each pixel in an image is classified into either predictable or unpredictable. For supervised learning, we construct a ground-truth dataset by representing uncertainty as quantised residuals and train a neural network to segment predictable and unpredictable regions. For unsupervised learning, we formulate an ad hoc loss function and apply the concept of transfer learning to estimate the uncertainty on the basis of a pre-trained neural network. The uncertainty analysers enable selective prediction and adaptive residual modulation, thereby improving the steganographic rate-distortion performance. We carry out an ablation study to clarify the contribution of the learning-based uncertainty analysers to the steganographic system, and compare their performance with that of a representative handcrafted statistical analyser. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER < 3 Algorithm 1: Encoding Input: x and m Output: x′ // pre-processing • [x̄,v] = scale⇓(x | α) • ω = concat(m,v)