Steganography schemes based on a deflection criterion for embedding posses a clear advantage against schemes based on heuristics as they provide a direct link between theoretical detectability and empirical performance. However, this advantage depends on the accuracy of the cover and stego model underlying the embedding scheme. In this work we propose an original steganography scheme based on a realistic model of sensor noise, taking into account the camera model, the ISO setting and the processing pipeline. Exploiting this statistical model allows us to take correlations between DCT coefficients into account. Several types of dependency models are presented, including a very general lattice model which accurately models dependencies introduced by a large class of processing pipelines of interest. We show in particular that the stego signal which minimizes the KL divergence under this model has a covariance proportional to the cover noise covariance. The resulting embedding scheme achieves state-of-the-art performances which go well beyond the current standards in side-informed JPEG steganography.