Because of the aliasing of the received waves and the sparse structure of the reflection signals, the temporal resolution is not good in acoustic detection of buried objects with low frequency waves. Thus, the problem of resolving the reflection position is notoriously ill-posed. In this paper, a maximum a posteriori estimator is presented to regularize the ill-posed problem, and an algorithm of particle swarm optimization is proposed to improve temporal resolution and reduce execution time. The results from research show that the method is efficient for using practical data in detecting objects buried in sand.