论文标题
分层合奏Kalman方法，具有稀疏性的广义伽玛超级主管
Hierarchical Ensemble Kalman Methods with Sparsity-Promoting Generalized Gamma Hyperpriors
论文作者
论文摘要
本文介绍了一个计算框架，该框架将灵活的正则化技术包含在集合卡尔曼方法中，以解决非线性逆问题。所提出的方法近似于层次贝叶斯模型的最大后验（MAP）估计值，其特征是有条件的高斯先验和广义伽玛超级主体。适当的超参数选择会产生促进性的正则化。我们提出了一种迭代算法用于地图估计，该算法在更新未知的Kalman方法和更新正规化中的超参数以促进稀疏性之间交替。在几个计算的示例中证明了我们方法的有效性，包括压缩传感和地下流动反向问题。
This paper introduces a computational framework to incorporate flexible regularization techniques in ensemble Kalman methods for nonlinear inverse problems. The proposed methodology approximates the maximum a posteriori (MAP) estimate of a hierarchical Bayesian model characterized by a conditionally Gaussian prior and generalized gamma hyperpriors. Suitable choices of hyperparameters yield sparsity-promoting regularization. We propose an iterative algorithm for MAP estimation, which alternates between updating the unknown with an ensemble Kalman method and updating the hyperparameters in the regularization to promote sparsity. The effectiveness of our methodology is demonstrated in several computed examples, including compressed sensing and subsurface flow inverse problems.
