Remote sensing of oceanographic data often yields incomplete coverage of the measurement domain. This can limit interpretability of the data and identification of coherent features informative of ocean dynamics. Several methods exist to fill gaps of missing oceanographic data and are often based on projecting the measurements onto basis functions or a statistical model. Herein, we use an information transport approach inspired from an image processing algorithm. This approach aims to restore gaps in data by advecting and diffusing information of features as opposed to the field itself. Since this method does not involve fitting or projection, the portions of the domain containing measurements can remain unaltered, and the method offers control over the extent of local information transfer. This method is applied to measurements of ocean surface currents by high frequency radars. This is a relevant application because data coverage can be sporadic, and filling data gaps can be essential to data usability. Application to two regions with differing spatial scale is considered. The accuracy and robustness of the method is tested by systematically blinding measurements and comparing the restored data at these locations to the actual measurements. These results demonstrate that even for locally large percentages of missing data points, the restored velocities have errors within the native error of the original data (e.g., <10% for velocity magnitude and <3% for velocity direction). Results were relatively insensitive to model parameters, facilitating a priori selection of default parameters for de novo applications. Plain Language SummaryResearchers measure many geophysical phenomena by remote sensing. One example is the measurement of the ocean surface currents by land-based radar stations. The data are useful for understanding coastal dynamics and how material is transported near the ocean surface. Based on various factors, these measurements are prone to incomplete coverage. The measured data field on the map is like an incomplete image with spatial gaps where data are missing. The incompleteness in the data field reduces its utility, especially for analyses that rely on continuous coverage such as tracking the movement of objects or identifying coherent flow patterns. Several methods have been proposed to restore lost data. Inspired by a technique from image processing, we developed a method to restore incomplete field data. This method uses equations that aim to transport features in the data field into missing parts, as opposed to directly transporting the field data itself. We present this method applied to remote measurements of ocean surface currents and evaluate its ability to restore missing information. However, this approach can be applied to restore other types of incomplete field measurements to improve usability and interpretation of such data.
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the correlated error, and the variance of the noise based on maximizing a marginal likelihood function. Our method involves suitably reducing the dimensionality of the hyperparameter space to simplify the estimation procedure to a univariate root-finding problem. Moreover, we derive bounds and asymptotes of the marginal likelihood function and its derivatives, which are useful to narrowing the initial range of the hyperparameter search. Using numerical examples, we demonstrate the computational advantages and robustness of the presented approach compared to traditional parameter optimization.
We develop heuristic interpolation methods for the functions $$t\mapsto \log \det \left( \textbf{A} + t\textbf{B} \right) $$ t ↦ log det A + t B and $$t\mapsto {{\,\textrm{trace}\,}}\left( (\textbf{A} + t\textbf{B})^{p} \right) $$ t ↦ trace ( A + t B ) p where the matrices $$\textbf{A}$$ A and $$\textbf{B}$$ B are Hermitian and positive (semi) definite and $$p$$ p and $$t$$ t are real variables. These functions are featured in many applications in statistics, machine learning, and computational physics. The presented interpolation functions are based on the modification of sharp bounds for these functions. We demonstrate the accuracy and performance of the proposed method with numerical examples, namely, the marginal maximum likelihood estimation for Gaussian process regression and the estimation of the regularization parameter of ridge regression with the generalized cross-validation method.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.