An extended Krylov subspace method for decoding edge-based compressed images by homogeneous diffusion

TL;DR

This paper introduces an extended Krylov subspace method for efficiently decoding edge-compressed images using homogeneous diffusion, offering a faster alternative to traditional heat equation solutions in image inpainting.

Contribution

It presents a novel numerical approach employing an extended Krylov subspace method for image decoding, improving efficiency in solving the heat equation at large times.

Findings

Significantly faster decoding of edge-compressed images.

Efficient solution of the heat equation at large times.

Applicable to inpainting-based lossy compression schemes.

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.