Information Embedding With Stegotext Reconstruction

In this paper, we consider stegotext reconstruction problem in information embedding. By adding the requirement of restoring the stegotext under certain fidelity criterion, we generalize the concept of reversible/irreversible information embedding. We focus on the stegotext reconstruction in a discrete memoryless host dependent attack channel, which can be regarded as a generalized Gel'fand-Pinsker problem with an input reconstruction constraint. For this problem, we prove an upper bound and a lower bound on its embedding capacity-distortion function, which is defined to describe the tradeoff between embedding information rate, host composition loss, and stegotext reconstruction distortion. In particular, our upper and lower bounds thus obtained match each other for the binary XOR attack channel with Hamming distortion and Costa's additive Gaussian attack channel with quadratic loss. We further consider a variant of this problem, where host signal is available at the encoder in a causal way. For this case, we completely characterize its capacity-distortion function.