Dirichlet Random Process-driven Bayesian Learning for Synthetic Aperture Radar Imagery via Gaussian Mixture Prior

In high-resolution synthetic aperture radar （SAR） imaging， the existing prior distributions derived via statistical methods are typically single and static. Consequently， the outcome of Bayesian inference depends on the specifics of any given problem. Therefore， existing models cannot solve problems with complex priors. Therefore， conventional methods fail to model detailed and refined features， which leads to incomplete retention of structural features of imaging targets and loss of weak scattering points. To address these issues， an SAR imaging algorithm based on Bayesian learning is proposed， utilizing a Dirichlet process-driven Gaussian mixture prior （DPGMP-Bayes）. Compared with conventional Bayesian modeling with random variables， statistical modeling methods that incorporate stochastic processes can model uncertainty with more flexibility. The Dirichlet process （DP） was employed to adaptively model the mixing weights of a Gaussian mixture model （GMM）. This approach further optimized the modeling process of the GMM in dynamically fitting complex prior distributions and achieved refined modeling of target features. Within the hierarchical Bayesian framework， the variational Bayes expectation maximization （VB-EM） algorithm was applied to adaptively infer hyperparameters. This technique enabled autonomous approximate inference of the posterior distribution， resulting in high-resolution imaging. Simulated and measured SAR data were used to compare the proposed approach with conventional imaging algorithms， and the results of qualitative and quantitative analyses validated that the proposed algorithm functioned as intended and exhibited superior performance compared with existing methods.