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Recent developments in compressed sensing have shown that if a signal has a low Kolmogorov complexity, then it can be reconstructed from a certain number of random projections. We study the distributed coding of correlated Gaussian sources. Both intra- and inter-correlation models are considered in the source models. Decoding schemes in which it is possible to exploit the existing correlation between the signals of interest to significantly improve reconstruction performance are presented. This is done in a fashion resembling distributed coding of digital sources.