In Wireless Sensor Networks, and especially in Wireless Multimedia Sensor Networks, scenarios are usually such that the signals acquired by various distributed sensors contain a shared common component and these intra- and inter-signal correlations are exploited in the theory of distributed source coding to compress signals more. These cases may occur in the applications and services that work with the smart spaces and the context aware networks. Similarly, distributed compressive sensing methods are developed to exploit the correlation between sparse signals. In this paper, a method based on the distributed compressive sensing is proposed to compress and reconstruct the signals of the sensors even for networks in which the data transmission is imperfect. Using the proposed method as like as other compressive sensing based compression scenario brings lower computational cost and amount of transmitted data, therefore lower bandwidth, power usage and more lifetime in sensor side. The proposed method can be used to develop a framework for services in which the shared component between sensors' signals is not changed for a while and this time is suitably large with respect to the network's sensing time interval.