A new lossy compression scheme for distributed and sparse sources under a low complexity encoding con- straint is proposed. This architecture is able to exploit both intra- and inter-signal correlations typical of sig- nals monitored, for example, by a wireless sensor net- work. In order to meet the low complexity constraint, the encoding stage is performed by a lossy distributed compressed sensing (CS) algorithm. The novelty of the scheme consists in the combination of lossy distributed source coding (DSC) and CS. More precisely, we pro- pose a joint CS reconstruction lter, which exploits the knowledge of the side information to improve the qual- ity of both the dequantization and the CS reconstruction steps. The joint use of CS and DSC allows to achieve large bit-rate savings for the same quality with respect to the non-distributed CS scheme, e.g. up to 1.2 bps in the cases considered in this paper. Compared to the DSC scheme (without CS), we observe a gain increasing with the rate for the same mean square error.