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Title: Scientific data interpolation with low dimensional manifold model

Abstract

Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.

Authors:
ORCiD logo [1];  [1]; ORCiD logo [2]; ORCiD logo [3];  [1];  [1]
  1. Univ. of California Los Angeles, Los Angeles, CA (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1407782
Grant/Contract Number:
AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 352; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Low dimensional manifold model (LDMM); Scientific data interpolation; Data compression; Regular and irregular sampling; Weighted graph Laplacian

Citation Formats

Zhu, Wei, Wang, Bao, Barnard, Richard C., Hauck, Cory D., Jenko, Frank, and Osher, Stanley. Scientific data interpolation with low dimensional manifold model. United States: N. p., 2017. Web. doi:10.1016/j.jcp.2017.09.048.
Zhu, Wei, Wang, Bao, Barnard, Richard C., Hauck, Cory D., Jenko, Frank, & Osher, Stanley. Scientific data interpolation with low dimensional manifold model. United States. doi:10.1016/j.jcp.2017.09.048.
Zhu, Wei, Wang, Bao, Barnard, Richard C., Hauck, Cory D., Jenko, Frank, and Osher, Stanley. Thu . "Scientific data interpolation with low dimensional manifold model". United States. doi:10.1016/j.jcp.2017.09.048.
@article{osti_1407782,
title = {Scientific data interpolation with low dimensional manifold model},
author = {Zhu, Wei and Wang, Bao and Barnard, Richard C. and Hauck, Cory D. and Jenko, Frank and Osher, Stanley},
abstractNote = {Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.},
doi = {10.1016/j.jcp.2017.09.048},
journal = {Journal of Computational Physics},
number = C,
volume = 352,
place = {United States},
year = {Thu Sep 28 00:00:00 EDT 2017},
month = {Thu Sep 28 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on September 28, 2018
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