Compressed sensing is an emerging field, which proposes that a small collection of linear projections of a sparse signal contains enough information for perfect reconstruction of the signal. In this thesis, we study the general problem of modeling and reconstructing spatially or temporally correlated sparse signals in a distributed scenario. The correlation among signals provides an additional information, which could be captured by joint sparsity models. After modeling the correlation, we propose two different reconstruction algorithms that are able to successfully exploit this additional information. The first algorithm is a very fast greedy algorithm, which is suitable for large scale problems and can exploit spatial correlation. The second algorithm is based on a thresholding algorithm and can exploit both the temporal and spatial correlation. We also generalize the standard joint sparsity model and propose a new model for capturing the correlation in the sensor networks.
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