Initial state reconstruction on graphs
Abstract
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.
Cite
@article{arxiv.2204.08081,
title = {Initial state reconstruction on graphs},
author = {Vo Anh Khoa and Mai Thanh Nhat Truong and Imhotep Hogan and Roselyn Williams},
journal= {arXiv preprint arXiv:2204.08081},
year = {2023}
}
Comments
12 pages, 42 figures, 2 tables