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.
翻译:本文介绍一个计算框架,将灵活的正规化技术纳入非线性反问题的混合Kalman方法中。拟议方法接近于以有条件的先质和普遍伽马超位为特点的高级巴伊西亚模型的后生估计值。对超参数的适宜选择可产生促进聚度的正规化。我们提议了一种双极算法,以混合Kalman方法更新未知数据,与更新常态中的超常参数以促进宽度相交。我们的方法的有效性体现在几个计算的例子中,包括压缩感测和地表下水流的反向问题。