The existing wireless sensor networks（ WSNs） data gathering methods cannot be ensure reliability of data gathering with low cost. To solve this problem

Based on the theory of compressive sensing（ CS）

sparse matrix based on exponential kernel function and measurement matrix based on quasicyclic low density parity check（ LDPC） code are designed to be used for data acquisition of node. Maximization of network lifetime is target

the measurement value transmission problem is modeled as the Hamilton loop problem

and a data gathering path optimization algorithm based on tree decomposition is proposed. Simulation results show that the performance of the proposed scheme is better than the typical data gathering methods in terms of data reconstruction error and energy consumption.