Theoretical limits to sensitivity and resolution in impedance imaging

Abstract

In any practical impedance imaging system it is important to be able to predict the image quality which can be expected from particular measurements. It is of interest both to establish the smallest object that can be detected for a certain noise level and to determine the maximum resolution for a certain number of electrodes. In impedance imaging this is not straightforward. The reason is that the resolution and the accuracy of an image which represents a conductive region are related to the number of electrodes and to the noise on the measurements. They also vary with position in the image and depend on the particular distribution of conductivity itself. It is therefore not possible, in general, to make quantitative statements about the resolution and accuracy. It is of course possible to make qualitative statements, but they are not of much use in any particular situation. Formulations are presented here which do allow quantitative assessment of the resolution and accuracy in a certain class of conductive regions. The regions to which they apply are two-dimensional and have a circular boundary shape. The details of the approach are included, both mathematically and descriptively. The quantitative improvement in image quality which can be obtained by reducing the noise, is shown both in terms of accuracy and resolution. The limit to the improvement in quality which can be obtained by taking unlimited independent measurements (i.e. using an unlimited number of electrodes) is calculated. It is shown how to predict the smallest sized object that can just be detected by measurements with a known level of noise.