Identification of an inclusion in multifrequency electric impedance tomography. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Ammari, Habib; Triki, Faouzi
• Is Part Of: Communications in partial differential equations. Volume 42:Issue 1(2017)
• Page Start: 159
• Page End: 177
• Publication Date: 2017-01-02
• Subjects: Electric impedance tomography -- inverse problems -- stability estimates; Primary: 35R30; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2016.1258578
• Languages: English
• ISSNs: 0360-5302

Abstract

ABSTRACT: The multifrequency electrical impedance tomography is considered to image a conductivity inclusion inside a homogeneous background medium by injecting one current. An original spectral decomposition of the solution of the forward conductivity problem is used to retrieve the Cauchy data corresponding to the extreme case of perfect conductor. Using results based on the unique continuation, we then prove the uniqueness of multifrequency electrical impedance tomography and obtain rigorous stability estimates. Our results in this paper are quite surprising in inverse conductivity problem since in general infinitely many input currents are needed to obtain the uniqueness in the determination of the conductivity.