Bayesian matrix decomposition with hierarchical Gaussian mixture model for complex reverberation suppression in active sonar detection

Moving target detection using active sonar systems is an effective approach for underwater safety monitoring, where complex reverberation from the seafloor, water surface, and water column can substantially degrade detection performance. Robust principal component analysis exploits the low-rank structure of reverberation and the sparsity of moving targets in multi-frame sonar images and has become a widely adopted technique for reverberation suppression. However, the performance of existing optimization-based suppression methods is constrained by the manual selection of the regularization parameter. To overcome this limitation, this paper formulates reverberation suppression for moving target detection within a Bayesian framework. The low-rank component is characterized using a hierarchical Gaussian Wishart distribution, while the non-low-rank components are represented by a Gaussian mixture model. This prior formulation more effectively captures the complex characteristics of reverberation interference. Variational Bayesian inference is applied to perform matrix decomposition, with a generalized approximate message passing algorithm introduced to avoid large-scale matrix inversions. After estimating the non-low-rank components, the moving target component is directly extracted. In addition, nonlinear accumulation is employed on the moving target component to derive the target trajectory. Experiments conducted on four different target datasets show that the proposed method achieves superior detection performance compared with other methods.