Abstract: Considering the application scenario of decentralized data collection in wireless sensor networks (WSNs), a distributed data reconstruction algorithm based on Jacobi ADMM (alternating direction method of multipliers) for compressed sensing is proposed by adopting the JSM-1 (joint sparse model-1) model in the distributed compressed sensing (DCS) theory. Through exchanging the common information among cluster heads to determine the common components in the correlated sensed data and update the innovation components in each cluster head, the compressed sensed data in WSNs are reconstructed in a distributed way. The data collection operation in wireless sensor networks is firstly abstracted as a distributed optimization problem. In order to avoid non-convergence in the distributed data reconstruction process, a proximal component is then introduced into the aforementioned optimization problem with the goal of converting the sub-problem of the optimization objective function into its strictly convex form. After that, the ADMM method is utilized to solve the data reconstruction problem. Both the synthetic dataset and the real world datasets are used in the experiments to verify the performance of the proposed algorithm. Experimental results show that the proposed data reconstruction algorithm can provide higher data reconstruction accuracy than the state of the art data reconstruction algorithms.