The Experts below are selected from a list of 242073 Experts worldwide ranked by ideXlab platform
Werner A Stahel - One of the best experts on this subject based on the ideXlab platform.
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stochastic partial differential equation based modelling of large space time data sets
Journal of The Royal Statistical Society Series B-statistical Methodology, 2015Co-Authors: Fabio Sigrist, Hans R Kunsch, Werner A StahelAbstract:type="main" xml:id="rssb12061-abs-0001"> Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection–diffusion partial differential equation provides a flexible model class for spatiotemporal processes which is computationally feasible also for large data sets. The Gaussian process defined through the stochastic partial differential equation has, in general, a non-separable covariance structure. Its parameters can be physically interpreted as explicitly modelling phenomena such as transport and diffusion that occur in many natural processes in diverse fields ranging from environmental sciences to ecology. To obtain computationally efficient statistical algorithms, we use spectral methods to solve the stochastic partial differential equation. This has the advantage that approximation errors do not accumulate over time, and that in the spectral space the computational cost grows linearly with the dimension, the total computational cost of Bayesian or frequentist inference being dominated by the fast Fourier transform. The model proposed is applied to post-processing of precipitation forecasts from a numerical weather prediction model for northern Switzerland. In contrast with the raw forecasts from the numerical model, the post-processed forecasts are calibrated and quantify prediction uncertainty. Moreover, they outperform the raw forecasts, in the sense that they have a lower mean absolute error.
Xiangfeng Yang - One of the best experts on this subject based on the ideXlab platform.
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uncertain partial differential equation with application to heat conduction
Fuzzy Optimization and Decision Making, 2017Co-Authors: Xiangfeng YangAbstract:This paper first presents a tool of uncertain partial differential equation, which is a type of partial differential equations driven by Liu processes. As an application of uncertain partial differential equation, uncertain heat equation whose noise of heat source is described by Liu process is investigated. Moreover, the analytic solution of uncertain heat equation is derived and the inverse uncertainty distribution of solution is explored. This paper also presents a paradox of stochastic heat equation.
Fabio Sigrist - One of the best experts on this subject based on the ideXlab platform.
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stochastic partial differential equation based modelling of large space time data sets
Journal of The Royal Statistical Society Series B-statistical Methodology, 2015Co-Authors: Fabio Sigrist, Hans R Kunsch, Werner A StahelAbstract:type="main" xml:id="rssb12061-abs-0001"> Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection–diffusion partial differential equation provides a flexible model class for spatiotemporal processes which is computationally feasible also for large data sets. The Gaussian process defined through the stochastic partial differential equation has, in general, a non-separable covariance structure. Its parameters can be physically interpreted as explicitly modelling phenomena such as transport and diffusion that occur in many natural processes in diverse fields ranging from environmental sciences to ecology. To obtain computationally efficient statistical algorithms, we use spectral methods to solve the stochastic partial differential equation. This has the advantage that approximation errors do not accumulate over time, and that in the spectral space the computational cost grows linearly with the dimension, the total computational cost of Bayesian or frequentist inference being dominated by the fast Fourier transform. The model proposed is applied to post-processing of precipitation forecasts from a numerical weather prediction model for northern Switzerland. In contrast with the raw forecasts from the numerical model, the post-processed forecasts are calibrated and quantify prediction uncertainty. Moreover, they outperform the raw forecasts, in the sense that they have a lower mean absolute error.
Shuaijie Li - One of the best experts on this subject based on the ideXlab platform.
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A Novel Nonlinear Second Order Hyperbolic partial differential equation-Based Image Restoration Algorithm With Directional Diffusion
IEEE Access, 2020Co-Authors: Shuaijie LiAbstract:Recently, variational and partial differential equation (PDE)-based algorithms have become very important for image restoration. In this study, we propose a new second order hyperbolic PDE model based on directional diffusion for image restoration. This hyperbolic PDE restoration model can simply diffuse along the edge's tangential direction in the observed image, thereby removing noise while preserving the image edges and fine details, which avoids the staircase effect in the restored image. An effective numerical scheme is proposed for handling the computation of our approach using the finite difference method. Successful image restoration experiments demonstrated that the proposed second order hyperbolic PDE-based model obtains superior performance compared with other models at preserving edges and it avoids the staircase effect.
Christine Fernandez-maloigne - One of the best experts on this subject based on the ideXlab platform.
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Regularization of multivalued images by means of a wavelet-based partial differential equation
2007 15th European Signal Processing Conference, 2007Co-Authors: Aldo Maalouf, Philippe Carré, Bertrand Augereau, Christine Fernandez-maloigneAbstract:In this work, a wavelet-based anisotropic diffusion partial differential equation (PDE) is developed. The new model makes use of a multiscale structure tensor as an extension of the single-scale structure tensor proposed by Di Zenzo. The multiscale structure tensor allows for accumulating multiscale gradient information of local regions. Thus, averaging properties are maintained while preserving edge structure. This structure tensor is used in an anisotropic diffusion process of multispectral images, namely, in the Perona-Malik model. Therefore, a more efficient and accurate formulation for edge-preserving diffusion is obtained.
