Scientific Data Interpolation with Low Dimensional Manifold Model
This work provides a general interpolation method for scientific data with missing information, but the approach is incremental as it applies existing manifold regularization to a broader range of data types.
The paper proposes a low-dimensional manifold model for interpolating scientific data from regular and irregular samplings with significant missing information, achieving effective data compression and interpolation across various scientific fields.
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.