# Image Reconstruction Requirements for Short-Range Inductive Sensors Used in Single-Coil MIT

## TL;DR

This paper discusses how to reconstruct images using a single inductive sensor in magnetic induction tomography, focusing on unique challenges like distance-related signal loss and depth-dependent regularization.

## Contribution

The paper introduces a novel regularization approach using a 2-term Sobolev norm for image reconstruction in single-coil MIT.

## Key findings

- Inductive loss measurements require subtraction of infinite-separation loss for accurate reconstruction.
- A 2-term Sobolev norm regularization improves image reconstruction by accounting for depth-dependent conductivity.
- The method was tested on a 4.3 cm thick phantom with bone-like features in agarose gel.

## Abstract

MIT (magnetic induction tomography) image reconstruction from data acquired with a single, small inductive sensor has unique requirements not found in other imaging modalities. During the course of scanning over a target, measured inductive loss decreases rapidly with distance from the target boundary. Since inductive loss exists even at infinite separation due to losses internal to the sensor, all other measurements made in the vicinity of the target require subtraction of the infinite-separation loss. This is accomplished naturally by treating infinite-separation loss as an unknown. Furthermore, since contributions to inductive loss decline with greater depth into a conductive target, regularization penalties must be decreased with depth. A pair of squared L2 penalty norms are combined to form a 2-term Sobolev norm, including a zero-order penalty that penalizes solution departures from a default solution and a first-order penalty that promotes smoothness. While constraining the solution to be non-negative and bounded from above, the algorithm is used to perform image reconstruction on scan data obtained over a 4.3 cm thick phantom consisting of bone-like features embedded in agarose gel, with the latter having a nominal conductivity of 1.4 S/m.