On Scientific Data and Image Compression Based on Adaptive Higher-Order FEM

We present a novel compression algorithm for 2D scientific data and images based on exponentially-convergent adaptive higher-order finite element methods (FEM). So far, FEM has been used mainly for the solution of partial differential equations (PDE), but we show that it can be applied to data and image compression easily. The adaptive compression algorithm is trivial compared to adaptive FEM algorithms for PDE since the error estimation step is not present. The method attains extremely high compression rates and is able to compress a data set or an image with any prescribed error tolerance. Compressed data and images are stored in the standard FEM format, which makes it possible to analyze them using standard PDE visualization software. Numerical examples are shown. The method is presented in such a way that it can be understood by readers who may not be experts of the finite element method.