Solving Image PDEs with a Shallow Network

TL;DR

This paper introduces a shallow learnable filtering framework called BLADE for solving PDEs in image processing, achieving efficient and accurate results at coarse resolutions compared to traditional methods.

Contribution

It demonstrates that BLADE can effectively solve PDEs in imaging tasks, reducing computational costs and improving stability over classical numerical approaches.

Findings

BLADE operates reliably at coarse grid resolutions.

The approach is more efficient than classical PDE solvers.

It is applicable to various image processing problems.

Abstract

Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for solving PDEs tend to require very fine grid resolution for stability, and as a result have impractically high computational cost. This work applies BLADE (Best Linear Adaptive Enhancement), a shallow learnable filtering framework, to PDE solving, and shows that the resulting approach is efficient and accurate, operating more reliably at coarse grid resolutions than classical methods. As such, the model can be flexibly used for a wide variety of problems in imaging.