Sampling and reconstruction of diffusive fields on graphs

Reddy, S and Chepuri, SP (2019) Sampling and reconstruction of diffusive fields on graphs. In: 7th IEEE Global Conference on Signal and Information Processing, GlobalSIP 2019, 11-14, November 2019, Canada.

PDF iee_nov_2019.pdf - Published Version Restricted to Registered users only Download (886kB) | Request a copy

Abstract

In this paper, the focus is on the reconstruction of a diffusive field and the localization of the underlying driving sources on arbitrary graphs by observing a significantly smaller subset of vertices of the graph uniformly in time. Specifically, we focus on the heat diffusion equation driven by an initial field and an external time-invariant input. When the underlying driving sources are modeled as an initial field or external input, the sources (hence the diffusive field) can be recovered from the subsampled observations without imposing any band-limiting or sparsity constraints. When the diffusion is induced by both the initial field and external input, then the field and sources can be recovered from the subsampled observations, however, by imposing band-limiting constraints on either the initial field or external input. For heat diffusion on graphs, we can compensate for the unobserved vertices with the temporal samples at the observed vertices. If the observations are noiseless, then the recovery is exact. Nonetheless, the developed least squares estimators perform reasonably well with noisy observations. We apply the developed theory for localizing and recovering hot spots on a rectangular metal plate with a cavity.

Item Type:	Conference Paper
Publication:	GlobalSIP 2019 - 7th IEEE Global Conference on Signal and Information Processing, Proceedings
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	cited By 0; Conference of 7th IEEE Global Conference on Signal and Information Processing, GlobalSIP 2019 ; Conference Date: 11 November 2019 Through 14 November 2019; Conference Code:157155
Keywords:	Diffusion; Graphic methods; Plate metal; Recovery; Signal processing, Band-limited signal; Graph samplings; Heat diffusion equations; Heat diffusions; Least-squares estimator; Sampling and reconstruction; Source localization; Sparsity constraints, Graph theory
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	13 Aug 2020 10:14
Last Modified:	13 Aug 2020 10:14
URI:	http://eprints.iisc.ac.in/id/eprint/64662

Actions (login required)

View Item