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:

 Univ. of California Los Angeles, Los Angeles, CA (United States)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 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) (SC21)
 OSTI Identifier:
 1407782
 Alternate Identifier(s):
 OSTI ID: 1549289
 Grant/Contract Number:
 AC0500OR22725; DeAC0500OR22725; DOESC0013838
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 352; Journal Issue: C; Journal ID: ISSN 00219991
 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. https://www.osti.gov/servlets/purl/1407782.
@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 = {2017},
month = {9}
}
Web of Science
Works referenced in this record:
Exemplarbased interpolation of sparsely sampled images
dataset, January 2013
 Facciolo, Gabriele; Arias, Pablo
 Figshare