Resolution Guarantees in Electrical Impedance Tomography

Abstract

Electrical impedance tomography (EIT) uses current-voltage measurements on the surface of an imaging subject to detect conductivity changes or anomalies. EIT is a promising new technique with great potential in medical imaging and non-destructive testing. However, in many applications, EIT suffers from inconsistent reliability due to its enormous sensitivity to modeling and measurement errors. In this work, we show that it is principally possible to give rigorous resolution guarantees in EIT even in the presence of systematic and random measurement errors. We derive a constructive criterion to decide whether a desired resolution can be achieved in a given measurement setup. Our results cover the case where anomalies of a known minimal contrast in a subject with imprecisely known background conductivity are to be detected from noisy measurements on a number of electrodes with imprecisely known contact impedances. The considered settings are still idealized in the sense that the shape of the imaging subject has to be known and the allowable amount of uncertainty is rather low. Nevertheless, we believe that this may be a starting point to identify new applications and to design and optimize measurement setups in EIT.

Interpolation of missing electrode data in electrical impedance tomography

“…For a fixed reconstruction grid, the monotonicity method will show the support of the conductivity difference up to the grid resolution in the limit of noiseless data and infinitely many electrodes. But it not yet clear how to choose an optimal reconstruction grid for a given amount of noise and number of electrodes (see however [33] for a method to evaluate whether certain reconstruction guarantees hold true on a given grid).…”

“…Still, in that case certain rigorous properties can be guaranteed, cf. [33], and rigorously justified methods have successfully been applied to real data situations, cf., e.g. [4,31,76].…”

Combining frequency-difference and ultrasound modulated electrical impedance tomography

“…Moreover, monotonicity arguments also allow for worst-case testing and resolution guarantees (cf. [37]) which might be helpful in relaxing the idealistic assumptions in future studies.…”

Experimental Study of Thermo-acoustic Imaging with the Current Injection

“…In the medical field, the electrical impedance tomography has the advantage of early diagnosis [1][2], in order to solve the problem of the low resolution [3] the coupling imaging technologies with multi-physical fields are proposed. The combination of the electromagnetics with the ultrasound is an emerging multiphysical field imaging with both of high contrast and high resolution, such as magneto-acoustic tomography with magnetic induction(MAT-MI) [4][5][6], microwave induced thermo-acoustic imaging(MI-TAI) [7] and magnetically mediated thermoacoustic imaging(MM-TAI) [8][9].…”