Scientific data interpolation with low dimensional manifold model

- A low dimensional manifold model is applied to the interpolation of scientific data from sparse sampling.
- The low dimensionality of the patch manifold for general scientific data sets is used as a regularizer.
- The proposed algorithm consistently outperforms other state-of-the-art methods in this field.
- The performance of the proposed method as a data compression technique is compared to other standard methods.

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.