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Stochastic parameterizations are increasingly being used to represent the uncertainty associated with model errors in ensemble forecasting and data assimilation. One of the challenges associated with the use of these parameterizations is…

The extended Kalman filter (EKF) is a widely adopted method for sensor fusion in navigation applications. A crucial aspect of the EKF is the online determination of the process noise covariance matrix reflecting the model uncertainty. While…

The non-stationary nature of electroencephalography (EEG) signals makes an EEG-based brain-computer interface (BCI) a dynamic system, thus improving its performance is a challenging task. In addition, it is well-known that due to…

This paper develops an efficient implementation of the ensemble Kalman filter based on a modified Cholesky decomposition for inverse covariance matrix estimation. This implementation is named EnKF-MC. Background errors corresponding to…

Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available…

When solving inverse problems, one increasingly popular approach is to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative…

Robustness against data inconsistencies, imaging artifacts and acquisition speed are crucial factors limiting the possible range of applications for magnetic resonance imaging (MRI). Therefore, we report a novel calibrationless parallel…

The main contribution of this paper is an invariant extended Kalman filter (EKF) for visual inertial navigation systems (VINS). It is demonstrated that the conventional EKF based VINS is not invariant under the stochastic unobservable…

We introduce a practical method for incorporating equality and inequality constraints in global optimization methods based on stochastic interacting particle systems, specifically consensus-based optimization (CBO) and ensemble Kalman…

Ensemble Kalman filter (EnKF) is an important data assimilation method for high dimensional geophysical systems. Efficient implementation of EnKF in practice often involves the localization technique, which updates each component using only…

The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations…

Solving inverse problems without the use of derivatives or adjoints of the forward model is highly desirable in many applications arising in science and engineering. In this paper, we propose a new version of such a methodology, a framework…

This paper proposes new methodology for sequential state and parameter estimation within the ensemble Kalman filter. The method is fully Bayesian and propagates the joint posterior density of states and parameters over time. In order to…

Electrical impedance tomography (EIT) is a noninvasive medical imaging modality utilizing the current-density/voltage data measured on the surface of the subject. Calder\'on's method is a relatively recent EIT imaging algorithm that is…

Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less…

Data assimilation (DA) integrates numerical model forecasts with observations to achieve the optimal state estimation. Ensemble-based methods, such as the ensemble Kalman filter (EnKF), are widely used for state estimation for…

Estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns, market mi- crostructure noise and jumps. One technique for addressing both asynchronous returns and market microstructure…

Because of physical assumptions and numerical approximations, low-order models are affected by uncertainties in the state and parameters, and by model biases. Model biases, also known as model errors or systematic errors, are difficult to…

Full-waveform inversion (FWI) is a powerful geophysical imaging technique that infers high-resolution subsurface physical parameters by solving a non-convex optimization problem. However, due to limitations in observation, e.g., limited…

Unsupervised video-based surgical instrument segmentation has the potential to accelerate the adoption of robot-assisted procedures by reducing the reliance on manual annotations. However, the generally low quality of optical flow in…