Improved distributed compressed sensing for smooth signals in wireless sensor networks

The technology of the distributed compressed sensing is thought as an extension of compressed sensing and it makes applying multiple signals into compressed sensing possible. A vital issue in distributed compressed sensing is to minimize the difference between the original signal and the recovery signal. In this paper, we improve the distributed compressed sensing for smooth signals in wireless sensor networks. Firstly, we put forward a new weighted method to obtain the common component of all signals, and then one method of lossy coding for shortening the length of common component is proposed. Most importantly, we improve the calculation formula of the distributed compressed sensing to ensure that the common component can be received losslessly. The numerical results show that, comparing with the distributed compressed sensing, the improved distributed compressed sensing not only can use much fewer measurements to recover the original signal, but also enable the effect of signal recovery to be better than that of traditional distributed compressed sensing.