Tomographic imaging of inhomogeneous non-local media using fractional order models

TL;DR

This paper introduces a tomographic imaging framework that employs fractional-order models to effectively image inhomogeneous media with non-local energy transport, capturing anomalous diffusion phenomena that traditional models miss.

Contribution

It develops a novel fractional-order modeling approach for tomographic imaging of non-local media, demonstrating its effectiveness through numerical simulations.

Findings

Fractional models improve imaging resolution in non-local media.

Properly accounting for fractional behavior enables successful reconstruction.

Traditional models fail to capture anomalous diffusion phenomena.

Abstract

We investigate a generalized tomographic imaging framework applicable to a class of inhomogeneous media characterized by non-local diffusive energy transport. Under these conditions, the transport mechanism is well described by fractional-order continuum models capable of capturing anomalous diffusion that would otherwise remain undetected when using traditional integer-order models. Although the underlying idea of the proposed framework is applicable to any transport mechanism, the case of fractional heat conduction is presented as a specific example to illustrate the methodology. By using numerical simulations, we show how complex inhomogeneous media involving non-local transport, can be successfully imaged if fractional order models are used. In particular, results will show that by properly recognizing and accounting for the fractional character of the host medium not only allows achieving increased resolution but, in case of strong and spatially distributed non-locality, it represents the only viable approach to achieve a successful reconstruction.