We investigate the problem of recovering source information from an incomplete set of network coded data with help of prior information about the sources. This problem naturally arises in wireless networks, where the number of network coded packets available at the receiver may not be sufficient for exact decoding due to channel dynamics or timing constraints, for example. We study the theoretical performance of such systems under maximum a posteriori (MAP) decoding and examine the influence of the data priors and in particular source correlation on the decoding performance. We also propose a low complexity iterative decoding algorithm based on message passing for decoding the network coded data in the case of pairwise linearly correlated source data. Our algorithm operates on a graph that captures the network coding constraints, while the knowledge about the source correlation is directly incorporated in the messages exchanged over the graph. We test the proposed method on both synthetic data and correlated image sequences and demonstrate that the prior knowledge about the statistical properties of the sources can be effectively exploited at the decoder in order to provide a good reconstruction of the transmitted data.