KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Computer Science Program
Visual Computing Center (VCC)
Permanent link to this recordhttp://hdl.handle.net/10754/575790
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AbstractWe introduce a new type of multi-resolution image pyramid for high-resolution images called sparse pdf maps (sPDF-maps). Each pyramid level consists of a sparse encoding of continuous probability density functions (pdfs) of pixel neighborhoods in the original image. The encoded pdfs enable the accurate computation of non-linear image operations directly in any pyramid level with proper pre-filtering for anti-aliasing, without accessing higher or lower resolutions. The sparsity of sPDF-maps makes them feasible for gigapixel images, while enabling direct evaluation of a variety of non-linear operators from the same representation. We illustrate this versatility for antialiased color mapping, O(n) local Laplacian filters, smoothed local histogram filters (e.g., median or mode filters), and bilateral filters. © 2012 ACM.
CitationHadwiger, M., Sicat, R., Beyer, J., Krüger, J., & Möller, T. (2012). Sparse PDF maps for non-linear multi-resolution image operations. ACM Transactions on Graphics, 31(6), 1–12. doi:10.1145/2366145.2366152
JournalACM Transactions on Graphics
Conference/Event nameProceedings of ACM SIGGRAPH Asia 2012
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Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilationHoang, Truong-Vinh; Krumscheid, Sebastian; Matthies, Hermann G.; Tempone, Raul (arXiv, 2021-06-15) [Preprint]Filtering is a data assimilation technique that performs the sequential inference of dynamical systems states from noisy observations. Herein, we propose a machine learning-based ensemble conditional mean filter (ML-EnCMF) for tracking possibly high-dimensional non-Gaussian state models with nonlinear dynamics based on sparse observations. The proposed filtering method is developed based on the conditional expectation and numerically implemented using machine learning (ML) techniques combined with the ensemble method. The contribution of this work is twofold. First, we demonstrate that the ensembles assimilated using the ensemble conditional mean filter (EnCMF) provide an unbiased estimator of the Bayesian posterior mean, and their variance matches the expected conditional variance. Second, we implement the EnCMF using artificial neural networks, which have a significant advantage in representing nonlinear functions over high-dimensional domains such as the conditional mean. Finally, we demonstrate the effectiveness of the ML-EnCMF for tracking the states of Lorenz-63 and Lorenz-96 systems under the chaotic regime. Numerical results show that the ML-EnCMF outperforms the ensemble Kalman filter.
A Particle Filter-based Adaptive Inflation Scheme for the Ensemble Kalman FilterAit-El-Fquih, Boujemaa; Hoteit, Ibrahim (Quarterly Journal of the Royal Meteorological Society, Wiley, 2020-01-24) [Article]An adaptive covariance inflation scheme is proposed for the ensemble Kalman filter (EnKF) to mitigate for the loss of ensemble variance. Adaptive inflation methods are mostly based on a Bayesian approach, which considers the inflation factor as a random variable with a given prior probability distribution, and then combines it with the inflation likelihood through Bayes’ rule to obtain its posterior distribution. In this work, we introduce a numerical implementation of this generic Bayesian approach that uses a particle filter (PF) to compute a Monte Carlo approximation of the inflation posterior distribution. To alleviate the sample attrition issue, the proposed PF employs an artificial dynamical model for the inflation factor based on the well-known smoothing-kernel West and Liu model. The positivity constraint on the inflation factor is further imposed through an inverse-Gamma transition density, whose parameters suggest analytical expressions. The resulting PF-EnKF scheme is straightforward to implement, and can use different number of particles in its EnKF and PF components. Numerical experiments are conducted with the Lorenz-96 model to demonstrate the effectiveness of the proposed method under various experimental scenarios.
Robust Ensemble Filtering and Its Relation to Covariance Inflation in the Ensemble Kalman FilterLuo, Xiaodong; Hoteit, Ibrahim (Monthly Weather Review, American Meteorological Society, 2011-12) [Article]A robust ensemble filtering scheme based on the H∞ filtering theory is proposed. The optimal H∞ filter is derived by minimizing the supremum (or maximum) of a predefined cost function, a criterion different from the minimum variance used in the Kalman filter. By design, the H∞ filter is more robust than the Kalman filter, in the sense that the estimation error in the H∞ filter in general has a finite growth rate with respect to the uncertainties in assimilation, except for a special case that corresponds to the Kalman filter. The original form of the H∞ filter contains global constraints in time, which may be inconvenient for sequential data assimilation problems. Therefore a variant is introduced that solves some time-local constraints instead, and hence it is called the time-local H∞ filter (TLHF). By analogy to the ensemble Kalman filter (EnKF), the concept of ensemble time-local H∞ filter (EnTLHF) is also proposed. The general form of the EnTLHF is outlined, and some of its special cases are discussed. In particular, it is shown that an EnKF with certain covariance inflation is essentially an EnTLHF. In this sense, the EnTLHF provides a general framework for conducting covariance inflation in the EnKF-based methods. Some numerical examples are used to assess the relative robustness of the TLHF–EnTLHF in comparison with the corresponding KF–EnKF method.