Network-based CS recovery is used for faster processing of large-scale data, as well as for sensor networks where the observation vector and sampling matrix are distributed. In this paper, we propose a distributed CS recovery algorithm, called DKIST, which is based on three concepts: diffusion strategy, iterative thresholding, and extended Kalman filtering. We investigate that the estimation is unbiased and minimum variance, and the entire network is stable. Also, we proposed some modifications on DKIST to lower communication bit rate and computation of complexity. Simulation results show that the proposed algorithms outperform the competing distributed CS recovery methods performance in terms of accuracy and speed of convergence.

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