Recent developments in compressed sensing have shown that if a signal can be compressed in some basis, then it can be reconstructed in such basis from a certain number ofrandom projections. Distributed compressed sensing, where several correlated signals are compressed in a distributed manner, has also been proposed in the literature. By allowing additional distortion, successful recovery in distributed compressed sensing can be achieved even if the projections are corrupted by noise. We extend this resultby showing that in addition to sparsity, it is possible to exploit prior knowledge existing in the correlation between the signals of interest to significantly improve reconstruction performance. This is done in a fashion resembling distributed coding of digital sources.