Using the characteristics of low rank for reverberation and sparsity for the target echo in multi-ping detection, the low-rank and sparsity decomposition method can effectively reduce reverberation. However, in the case of highly sparse reverberation or a stationary target, the distinctions in the characteristics between the reverberation and target echo become ambiguous. As a result, the reverberation reduction performance is degraded. To guarantee a meaningful decomposition based on the random orthogonal model and random sparsity model, the identifiability condition (IC) for the decomposition was derived from the perspective of the low-rank matrix and sparse matrix, respectively. According to the IC, sparsity compensation for the low-rank matrix was proposed to address the false alarm probability inflation (FAPI) induced by highly sparse reverberation. In addition, increasing the dimension of the sparse matrix was also proposed to manage the detection probability shrinkage caused by a stationary target. The robust reverberation reduction performance was validated via simulations and field experiments. It is demonstrated that FAPI can be eliminated by increasing the sparse coefficient of the low-rank matrix to 0.30 and a stationary target could be detected with a large ping number, i.e., a high dimension, of the sparse matrix.