Bounds on the size of an inclusion using the translation method for two-dimensional complex conductivity

Abstract

The size estimation problem in electrical impedance tomography is considered when the conductivity is a complex number and the body is two-dimensional. Upper and lower bounds on the volume fraction of the unknown inclusion embedded in the body are derived in terms of two pairs of voltage and current data measured on the boundary of the body. These bounds are derived using the translation method. We also provide numerical examples to show that these bounds are quite tight and stable under measurement noise.

15 pages, 5 figures, 5 tables

References in corpus (3)

• Minimization variational principles for acoustics, elastodynamics, and electromagnetism in lossy inhomogeneous bodies at fixed frequency
• Universal bounds on the electrical and elastic response of two-phase bodies and their application to bounding the volume fraction from boundary measurements
• Bounds on the volume fraction of 2-phase, 2-dimensional elastic bodies and on (stress, strain) pairs in composites