In a compressed sensing setup with jointly sparse, correlated data,we develop a distributed greedy algorithm called distributed predic-tive subspace pursuit. Based on estimates from neighboring sensornodes, this algorithm operates iteratively in two steps: first forminga prediction of the signal and then solving the compressed sensingproblem with an iterative linear minimum mean squared estimator.Through simulations we show that the algorithm provides better per-formance than current state-of-the-art algorithms.