Inpainting based image compression approaches, especially linear and
non-linear diffusion models, are an active research topic for lossy image
compression. The major challenge in these compression models is to find a small
set of descriptive supporting points, which allow for an accurate
reconstruction of the original image. It turns out in practice that this is a
challenging problem even for the simplest Laplacian interpolation model. In
this paper, we revisit the Laplacian interpolation compression model and
introduce two fast algorithms, namely successive preconditioning primal dual
algorithm and the recently proposed iPiano algorithm, to solve this problem
efficiently. Furthermore, we extend the Laplacian interpolation based
compression model to a more general form, which is based on principles from
bi-level optimization. We investigate two different variants of the Laplacian
model, namely biharmonic interpolation and smoothed Total Variation
regularization. Our numerical results show that significant improvements can be
obtained from the biharmonic interpolation model, and it can recover an image
with very high quality from only 5% pixels.

本文介绍了两种算法来高效地解决 Laplacian interpolation 压缩模型中的支持点选取问题，并将其扩展到了更为一般化的双层优化 Laplacian 模型，其中 biharmonic interpolation 表现出了更好的压缩效果。