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A. Tamburrino

Monotonicity based imaging methods for elliptic and parabolic inverse problems

In this paper we address the tomographic imaging of the electrical resistivity of material bodies by means of static or low frequency electromagnetic fields. The problem is treated in the framework of a recently proposed imaging method based on a monotonicity of the operator mapping a given resistivity distribution into the measured data. The monotonicity holds for elliptic problems such as Electrical Resistance Tomography (ERT). Here we prove that it is possible to extend the monotonicity to parabolic problems such as Magnetic Induction Tomography (MIT). Specifically, we prove that it is possible to construct a proper observable having the same monotonicity of ERT. In addition, a method for measuring this observable from time-domain MIT data is presented.

Journal of Inverse and Ill-posed Problems, Walter de Gruyter

Print ISSN: 0928-0219
Volume: 14, 09/2006
Pages: 633 - 642

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