Abstract: Measurement matrix construction is the key part of the moment of methods based on compressive sensing, and the measurement matrix constructed by random or uniform extraction will lack the important information in the impedance matrix, as well as the obtained measurement matrix is large in dimension and inefficient in solving. In order to effectively extract the key information in the impedance matrix to construct the measurement matrix, a novel measurement matrix construction method based on adaptive cross approximation (ACA) algorithm is proposed. First, the target is divided into blocks, and the weakest coupling with each block is identified and marked; then, the ACA algorithm is applied to compress the mutual impedance matrix between the marked blocks, and the row indexes generated in the process are used to extract the corresponding rows of the original impedance matrix to obtain the measurement matrix. Compared with the traditional method, the measurement matrix constructed by the new method is lower in dimension, and the calculation efficiency is significantly improved. Numerical results demonstrate the effectiveness of the new method.