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Wireless Sensor Networks (WSN) are mainly characterized by a potentially large number of distributed sensor nodes which collectively transmit information about sensed events to the sink. In this paper, we present a centralized generating algorithm running at the sink to obtain the distributed wavelet basis in WSN. And on this basis, Wavelet Transform-based Distributed Compressed Sensing (WTDCS) algorithm is proposed to compress and reconstruct sensor observations with spatial correlations. Finally, the analysis of relationship between reconstruction error and energy consumption in WTDCS is carried out by simulation. The results show that WTDCS can achieve high performance in terms of energy and reconstruction accuracy, as compared to conventional distributed wavelet transform algorithm.