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Existing fast algorithms for bilateral and nonlocal means filtering mostly work with grayscale images. They cannot easily be extended to high-dimensional data such as color and hyperspectral images, patch-based data, flow-fields, etc. In…
A long-standing challenge in multiple-particle-tracking is the accurate and precise 3D localization of individual particles at close proximity. One established approach for snapshot 3D imaging is point-spread-function (PSF) engineering, in…
We consider the Kalman-filtering problem with multiple sensors which are connected through a communication network. If all measurements are delivered to one place called fusion center and processed together, we call the process centralized…
Localization and tracking of a mobile node (MN) in non-line-of-sight (NLOS) scenarios, based on time of arrival (TOA) measurements, is considered in this work. To this end, we develop a constrained form of square root unscented Kalman…
This paper examines issues of data completion and location uncertainty, popular in many practical PDE-based inverse problems, in the context of option calibration via recovery of local volatility surfaces. While real data is usually more…
This paper is concerned with optimal control problems for control systems in continuous time, and interacting particle system methods designed to construct approximate control solutions. Particular attention is given to the linear quadratic…
The Kalman filter (KF) is a widely-used algorithm for tracking dynamic systems that are captured by state space (SS) models. The need to fully describe a SS model limits its applicability under complex settings, e.g., when tracking based on…
Controlled interacting particle systems such as the ensemble Kalman filter (EnKF) and the feedback particle filter (FPF) are numerical algorithms to approximate the solution of the nonlinear filtering problem in continuous time. The…
Template matching is a fundamental problem in computer vision with applications in fields including object detection, image registration, and object tracking. Current methods rely on nearest-neighbour (NN) matching, where the query feature…
Several variations of the Kalman filter algorithm, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are widely used in science and engineering applications. In this paper, we introduce two algorithms of…
Filtering - the task of estimating the conditional distribution for states of a dynamical system given partial and noisy observations - is important in many areas of science and engineering, including weather and climate prediction.…
Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the…
The widely-used Extended Kalman Filter (EKF) provides a straightforward recipe to estimate the mean and covariance of the state given all past measurements in a causal and recursive fashion. For a wide variety of applications, the EKF is…
The $k$-Facility Location problem is a generalization of the classical problems $k$-Median and Facility Location. The goal is to select a subset of at most $k$ facilities that minimizes the total cost of opened facilities and established…
The location of a robot is a key aspect in the field of mobile robotics. This problem is particularly complex when the initial pose of the robot is unknown. In order to find a solution, it is necessary to perform a global localization. In…
This paper is concerned with sequential filtering based stochastic optimization (FSO) approaches that leverage a probabilistic perspective to implement the incremental proximity method (IPM). The present FSO methods are derived based on the…
Simultaneous Localization and Mapping (SLAM) algorithms perform visual-inertial estimation via filtering or batch optimization methods. Empirical evidence suggests that filtering algorithms are computationally faster, while optimization…
Data assimilation (DA) for compressible flows with shocks is challenging because many classical DA methods generate spurious oscillations and nonphysical features near uncertain shocks. We focus here on the ensemble Kalman filter (EnKF). We…
For modelling geophysical systems, large-scale processes are described through a set of coarse-grained dynamical equations while small-scale processes are represented via parameterizations. This work proposes a method for identifying the…
The use of model order reduction techniques in combination with ensemble-based methods for estimating the state of systems described by nonlinear partial differential equations has been of great interest in recent years in the data…