Abstract

Bayesian inverse problems can be challenging to solve when working with partial and noisy data, particularly in high-dimensional and nonlinear settings. One commonly used method is ensemble Kalman filtering, which provides robust and computationally efficient estimations through Gaussian approximations. However, this method may not accurately approximate non-Gaussian posterior distributions. To address this issue, the tempered ensemble transform particle filter has been developed as an adaptive sequential Monte Carlo method that uses optimal transport mapping for resampling. This approach does not rely on assumptions about the posterior distribution, making it suitable for nonlinear non-Gaussian inverse problems. However, it is computationally complex and less robust than ensemble Kalman filtering for high-dimensional problems. To improve the accuracy and efficiency of this method, an entropy-inspired regularization factor to reduce computational costs through Sinkhorn iterations is introduced. Additionally, we incorporate an ensemble Kalman filtering proposal step before each sample update, resulting in a hybrid approach that further enhances the method’s robustness.