Initial state reconstruction on graphs

04/17/2022
by   Vo Anh Khoa, et al.
0

The presence of noise is an intrinsic problem in acquisition processes for digital images. One way to enhance images is to combine the forward and backward diffusion equations. However, the latter problem is well known to be exponentially unstable with respect to any small perturbations on the final data. In this scenario, the final data can be regarded as a blurred image obtained from the forward process, and that image can be pixelated as a network. Therefore, we study in this work a regularization framework for the backward diffusion equation on graphs. Our aim is to construct a spectral graph-based solution based upon a cut-off projection. Stability and convergence results are provided together with some numerical experiments.

READ FULL TEXT

page 2

page 9

page 10

research
03/08/2019

Stable Backward Diffusion Models that Minimise Convex Energies

Backward diffusion processes appear naturally in image enhancement and d...
research
09/15/2021

Backward diffusion-wave problem: stability, regularization and approximation

We aim at the development and analysis of the numerical schemes for appr...
research
08/09/2021

Natural Numerical Networks for Natura 2000 habitats classification by satellite images

Natural numerical networks are introduced as a new classification algori...
research
06/03/2019

A new nonlocal forward model for diffuse optical tomography

The forward model in diffuse optical tomography (DOT) describes how ligh...
research
06/17/2022

A Flexible Diffusion Model

Diffusion (score-based) generative models have been widely used for mode...
research
03/19/2021

Forward and Backward Bellman equations improve the efficiency of EM algorithm for DEC-POMDP

Decentralized partially observable Markov decision process (DEC-POMDP) m...
research
10/22/2020

Travelling wave solutions for fully discrete FitzHugh-Nagumo type equations with infinite-range interactions

We investigate the impact of spatial-temporal discretisation schemes on ...

Please sign up or login with your details

Forgot password? Click here to reset