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The interaction between free electrons and optical near fields is attracting increasing attention as a way to manipulate the electron wave function in space, time, and energy. Relying on currently attainable experimental capabilities, we…
In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able…
Ensemble Kalman inversion is a parallelizable derivative-free method to solve inverse problems. The method uses an ensemble that follows the Kalman update formula iteratively to solve an optimization problem. The ensemble size is crucial to…
Filtering is a widely used methodology for the incorporation of observed data into time-evolving systems. It provides an online approach to state estimation inverse problems when data is acquired sequentially. The Kalman filter plays a…
When light is passed through aberrated optical systems, the resulting degradation in amplitude and phase has deleterious effects, for example, on resolution in imaging, spot sizes in focussing, and the beam quality factor of the output…
Scanning transmission electron microscopy (STEM) has become the technique of choice for quantitative characterization of atomic structure of materials, where the minute displacements of atomic columns from high-symmetry positions can be…
The Kalman filter (KF) and the extended Kalman filter (EKF) are well established techniques for state estimation. However, the choice of the filter tuning parameters still poses a major challenge for the engineers [1]. In the present work,…
This work presents new results and understanding of the Ensemble Kalman filter (EnKF) for inverse problems. In particular, using a Lagrangian dual perspective we show that EnKF can be derived from the sample average approximation (SAA) of…
Simulation-based Dynamic Traffic Assignment models have important applications in real-time traffic management and control. The efficacy of these systems rests on the ability to generate accurate estimates and predictions of traffic states,…
The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the…
Automated experiments in scanning transmission electron microscopy (STEM) require rapid image segmentation to optimize data representation for human interpretation, decision-making, site-selective spectroscopies, and atomic manipulation.…
In this work, the trailing-edge shape of an airfoil is optimized to reduce the acoustic noise based on large-eddy simulation (LES). It is achieved by the ensemble Kalman method, which can enhance the optimization efficiency by using the…
Reconfigurable intelligent surface (RIS)-assisted orthogonal frequency division multiplexing (OFDM) systems have aroused extensive research interests due to the controllable communication environment and the performance of combating…
In inverse problems, the goal is to estimate unknown model parameters from noisy observational data. Traditionally, inverse problems are solved under the assumption of a fixed forward operator describing the observation model. In this…
The achievable instrumental performance of a scanning transmission electron microscope (STEM) is determined by the size and shape of the incident electron probe. The most important optical factor in achieving the optimum probe profile is…
The Ensemble Kalman Inversion (EKI) method is widely used for solving inverse problems, leveraging ensemble-based techniques to iteratively refine parameter estimates. Despite its versatility, the accuracy of EKI is constrained by the…
The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state…
Data assimilation provides algorithms for widespread applications in various fields. It is of practical use to deal with a large amount of information in the complex system that is hard to estimate. Weather forecasting is one of the…
The Kalman filter has been adopted in acoustic echo cancellation due to its robustness to double-talk, fast convergence, and good steady-state performance. The performance of Kalman filter is closely related to the estimation accuracy of…
Secondary electron (SE) imaging techniques, such as scanning electron microscopy and helium ion microscopy (HIM), use electrons emitted by a sample in response to a focused beam of charged particles incident at a grid of raster scan…