In order to solve the problem of redundancy and transmission energy consumption in the process of data acquisition in wireless sensor networks, a method for designing the measurement matrix of compressive sensing was proposed in this paper. The method is based on the linear representation theory of diagonal matrix orthogonal basis and the process of constructing the matrix is simple with short time, high sparsity and low redundancy, which is very suitable for the nodes with limited hardware resources. The simulation results show the measurement method based on the linear representation theory of diagonal matrix gains higher signal recovery rate compared with Gauss random matrix and part Hadamard matrix under the same signal reconstruction accuracy. This method in the paper greatly reduces the traffic of networks, saves the network energy consumption and prolongs the network life cycle.