狄利克雷过程驱动的高斯混合先验贝叶斯学习SAR成像

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

  • 摘要: 应用统计学方法进行合成孔径雷达(Synthetic Aperture Radar,SAR)高分辨成像时,目前的先验分布均为单一的、静态的,造成贝叶斯推断具有问题依赖性,对于复杂先验问题不可解,导致现有方法无法进行细节特征、精细化特征建模,成像目标结构特征保留不完整,弱散射点易丢失。针对以上问题,提出一种基于狄利克雷过程驱动的高斯混合先验贝叶斯(Dirichlet Process driven Gaussian Mixture Prior Bayes,DPGMP-Bayes)学习SAR成像算法。相比传统随机变量的贝叶斯建模,基于随机过程分析的统计建模方法具备更加灵活的不确定性建模能力,应用狄利克雷过程(Dirichlet Process,DP)可实现对高斯混合模型(Gaussian Mixture Model,GMM)混合权重的自适应建模,进而优化GMM动态拟合复杂先验分布的建模过程,实现目标特征的精细化建模。在分层贝叶斯框架下,通过变分贝叶斯期望最大化(Variational Bayes Expectation Maximization, VB-EM)算法对超参数进行自适应推断,实现模型后验分布的自主性近似推断,从而实现高分辨率成像。利用SAR仿真及实测数据与传统成像算法进行对比,从定性和定量角度分析验证算法的有效性及优越性。

     

    Abstract: 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.

     

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