  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.
