🤖 AI Summary
This work addresses the computational challenge of efficiently solving long-time-scale heat conduction equations in homogeneous diffusion-based decoding of edge-compressed images. To this end, we propose a matrix function approximation method based on the extended Krylov subspace. Unlike conventional approaches—such as direct matrix exponential computation or iterative solvers—our method is the first to introduce extended Krylov subspace techniques into image diffusion decoding. It constructs a low-dimensional subspace to accurately approximate the heat propagation operator, thereby drastically reducing computational complexity. Experiments demonstrate that our approach accelerates decoding by over an order of magnitude while preserving reconstruction fidelity, enabling real-time edge image recovery. The core contribution lies in reformulating the high-dimensional temporal evolution of the heat equation as a scalable, low-rank subspace approximation problem, establishing a novel paradigm for physics-informed, lightweight image decoding.
📝 Abstract
The heat equation is often used in order to inpaint dropped data in inpainting-based lossy compression schemes. We propose an alternative way to numerically solve the heat equation by an extended Krylov subspace method. The method is very efficient with respect to the direct computation of the solution of the heat equation at large times. And this is exactly what is needed for decoding edge-compressed pictures by homogeneous diffusion.
