Total variation regularization in Electric Impedance Tomography

Andrea Borsic

Thayer School, Dartmouth College.

Electric Impedance Tomography is a technique that involves estimating the conductivity and permittivity of and object from boundary measurements. The measurements are performed by applying a series of electrodes to the surface of the object under measurement, by passing some low frequency AC currents through some of the electrodes and by measuring the resulting potentials at the remaining electrodes. The problem of reconstructing the conductivity/permittivity profile, withing the object, from such measurements is ill-posed, and regularization techniques are needed in order to obtain meaningful images. Classical regularization techniques limit however the capability of reconstructing images with rapid spatial changes, such the ones occurring at the boundary of two materials with different properties, or at the interface between two different biological organs, or as the step change presented by abnormal tissue with respect to normal tissue. The talk will focus on the application of the Total Variation functional as a Tikhonov regularization functional, as this results in reconstruction algorithms that are able to describe step changes in the tomographic images.

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