Connecting Image Inpainting with Denoising in the Homogeneous Diffusion Setting

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Main Authors: Gaa, Daniel, Chizhov, Vassillen, Peter, Pascal, Weickert, Joachim, Adam, Robin Dirk
Format: Preprint
Published: 2023
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author Gaa, Daniel
Chizhov, Vassillen
Peter, Pascal
Weickert, Joachim
Adam, Robin Dirk
author_facet Gaa, Daniel
Chizhov, Vassillen
Peter, Pascal
Weickert, Joachim
Adam, Robin Dirk
contents While local methods for image denoising and inpainting may use similar concepts, their connections have hardly been investigated so far. The goal of this work is to establish links between the two by focusing on the most foundational scenario on both sides: the homogeneous diffusion setting. To this end, we study a denoising by inpainting (DbI) framework: It averages multiple inpainting results from different noisy subsets. We derive equivalence results between DbI on shifted regular grids and homogeneous diffusion filtering in 1D via an explicit relation between the density and the diffusion time. We also provide an empirical extension to the 2-D case. We present experiments that confirm our theory and suggest that it can also be generalized to diffusions with non-homogeneous data or non-homogeneous diffusivities. More generally, our work demonstrates that the hardly explored idea of data adaptivity deserves more attention: It can be as powerful as some popular models with operator adaptivity.
format Preprint
id arxiv_https___arxiv_org_abs_2309_13486
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Connecting Image Inpainting with Denoising in the Homogeneous Diffusion Setting
Gaa, Daniel
Chizhov, Vassillen
Peter, Pascal
Weickert, Joachim
Adam, Robin Dirk
Image and Video Processing
While local methods for image denoising and inpainting may use similar concepts, their connections have hardly been investigated so far. The goal of this work is to establish links between the two by focusing on the most foundational scenario on both sides: the homogeneous diffusion setting. To this end, we study a denoising by inpainting (DbI) framework: It averages multiple inpainting results from different noisy subsets. We derive equivalence results between DbI on shifted regular grids and homogeneous diffusion filtering in 1D via an explicit relation between the density and the diffusion time. We also provide an empirical extension to the 2-D case. We present experiments that confirm our theory and suggest that it can also be generalized to diffusions with non-homogeneous data or non-homogeneous diffusivities. More generally, our work demonstrates that the hardly explored idea of data adaptivity deserves more attention: It can be as powerful as some popular models with operator adaptivity.
title Connecting Image Inpainting with Denoising in the Homogeneous Diffusion Setting
topic Image and Video Processing
url https://arxiv.org/abs/2309.13486