Image Compression with Differential Equations

where well-engineered methods with high performance exist.
Partial differential equations (PDEs), however, have not much
been explored in this context so far. In my talk I will introduce
a framework for image compression that makes use of the
interpolation and inpainting qualities of linear and nonlinear
diffusion processes.

The basic idea behind these approaches is to store only a small
fraction of all pixels and to interpolate the missing information
by solving a suitable partial differential equation.

We will show that this PDE-based interpolation approach can lead to
results that outperform classical interpolation techniques such as
thin plate splines. We will discuss criteria for selecting the most
appropriate interpolation points. Experiments will be presented
that demonstrate that PDE-based image compression may give better
results than the JPEG standard, in particular if high compression
rates are needed.