Bat algorithm, as an optimization strategy of the observation matrix, has been widely used. Observation matrix has a direct impact on the reconstructed signal accuracy as a projection transformation matrix, and it has been widely used in various algorithms. However, for the traditional experimental process, randomly generated observation matrices often result in a larger reconstruction error and unstable reconstruction results. Therefore, it is a challenge to retain more feature information of the original signal and reduce reconstruction error. To obtain a more accurate reconstruction signal and less memory space, it is important to select an effective compression and reconstruction strategy. To solve this problem, an adaptive bat algorithm is proposed to optimize the observation matrix in this paper. For the adaptive bat algorithm, we design a dynamic adjustment strategy of the optimal radius to improve its global convergence ability. The results of our simulation experiments verify that, compared with other algorithms, it can effectively reduce the reconstruction error and has stronger robustness.