Ensemble Riemannian data assimilation over the Wasserstein space [PDF]
Nonlinear Processes in Geophysics, 2021 In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Euclidean distance used in classic data assimilation methodologies, the Wasserstein metric can capture the ...
S. K. Tamang +6 more
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Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves [PDF]
, 2015 We discuss a new notion of distance on the space of finite and nonnegative measures which can be seen as a generalization of the well-known Kantorovich-Wasserstein distance.
Liero, Matthias +2 more
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Target detection based on generalized Bures–Wasserstein distance
EURASIP Journal on Advances in Signal Processing, 2023 Radar target detection with fewer echo pulses in non-Gaussian clutter background is a challenging problem. In this instance, the conventional detectors using coherent accumulation are not very satisfactory.
Zhizhong Huang, Lin Zheng
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Detecting changes in forced climate attractors with Wasserstein distance [PDF]
Nonlinear Processes in Geophysics, 2017 The climate system can been described by a dynamical system and its associated attractor. The dynamics of this attractor depends on the external forcings that influence the climate.
Y. Robin, P. Yiou, P. Naveau
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Dimensional contraction via Markov transportation distance [PDF]
, 2013 It is now well known that curvature conditions \`a la Bakry-Emery are equivalent to contraction properties of the heat semigroup with respect to the classical quadratic Wasserstein distance.
Bolley, François +2 more
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Optimal transport bounds between the time-marginals of a multidimensional diffusion and its Euler scheme [PDF]
, 2015 In this paper, we prove that the time supremum of the Wasserstein distance between the time-marginals of a uniformly elliptic multidimensional diffusion with coefficients bounded together with their derivatives up to the order $2$ in the spatial ...
Alfonsi, Aurélien +2 more
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Generating Adversarial Samples With Constrained Wasserstein Distance
IEEE Access, 2019 In recent years, deep neural network (DNN) approaches prove to be useful in many machine learning tasks, including classification. However, small perturbations that are carefully crafted by attackers can lead to the misclassification of the images ...
Kedi Wang, Ping Yi, Futai Zou, Yue Wu
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Gromov-Hausdorff convergence of discrete transportation metrics [PDF]
, 2012 This paper continues the investigation of `Wasserstein-like' transportation distances for probability measures on discrete sets. We prove that the discrete transportation metrics on the d-dimensional discrete torus with mesh size 1/N converge, when $N\to\
Jan Maas, Mielke A., Nicola Gigli
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Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces [PDF]
, 2018 We develop tools to construct Lyapunov functionals on the space of probability measures in order to investigate the convergence to global equilibrium of a damped Euler system under the influence of external and interaction potential forces with respect ...
Carrillo, José A. +2 more
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MRWM: A Multiple Residual Wasserstein Driven Model for Image Denoising
IEEE Access, 2022 Residual histograms can provide valuable information for vision research. However, current image restoration methods have not fully exploited the potential of multiple residual histograms, especially their role as overall regularization constraints.
Rui-Qiang He, Wang-Sen Lan, Fang Liu
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