| Abstract: | 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. |
