Distinguishability revisited: depth dependent bounds on reconstruction quality in electrical impedance tomography

Abstract

The reconstruction problem in electrical impedance tomography is highly ill-posed, and it is often observed numerically that reconstructions have poor resolution far away from the measurement boundary but better resolution near the measurement boundary. The observation can be quantified by the concept of distinguishability of inclusions. This paper provides mathematically rigorous results supporting the intuition. Indeed, for a model problem lower and upper bounds on the distinguishability of an inclusion are derived in terms of the boundary data. These bounds depend explicitly on the distance of the inclusion to the boundary, i.e. the depth of the inclusion. The results are obtained for disk inclusions in a homogeneous background in the unit disk. The theoretical bounds are verified numerically using a novel, exact characterization of the forward map as a tridiagonal matrix.

25 pages, 6 figures

References in corpus (4)

• Monotonicity based shape reconstruction in electrical impedance tomography
• Resolution Guarantees in Electrical Impedance Tomography
• Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography
• Sparsity prior for electrical impedance tomography with partial data

Cited by in corpus (5)

• The regularized monotonicity method: detecting irregular indefinite inclusions
• Comparison of linear and non-linear monotononicity-based shape reconstruction using exact matrix characterizations
• Propagation and recovery of singularities in the inverse conductivity problem
• Optimal depth-dependent distinguishability bounds for electrical impedance tomography in arbitrary dimension
• Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps