By leveraging the high correlation between multi-ping echo data, low-rank and sparse decomposition methods are applied for reverberation suppression. Previous methods typically perform decomposition on the vectorized multi-ping echograph, which is obtained by stacking beamforming outputs from all directions in the same column. However, when the multi-ping correlation of beamforming outputs from different directions varies significantly due to the time-varying nature of the underwater acoustic channel, it becomes challenging to precisely capture the variations of the reverberation background. As a result, the performance of reverberation suppression is degraded. To alleviate this issue, we attempt to decompose the matrix formed by multi-ping beamforming outputs in different directions individually. The accelerated alternating projections method is used to estimate the steady reverberation for moving target detection. By exploiting the differences in spatio-temporal dimensions between moving targets and reverberation fluctuations, a weighted spatio-temporal density method with adaptive thresholding is used to further extract the target echoes. Field data were utilized to validate the effectiveness of the proposed method, and the experimental results demonstrated its superior robustness in an unstable reverberation-limited environment, maintaining an accurate estimation of steady reverberation.