The MUSIC algorithm for impedance tomography of small inclusions from discrete data. (17th August 2015)

• Record Type: Journal Article
• Authors: Lechleiter, A
• Is Part Of: Inverse problems. Volume 31:Number 9(2015:Sep.)
• Publication Date: 2015-08-17
• Subjects: Impedance Tomography -- MUSIC algorithm -- Point electrode model; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/9/095004
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider a point-electrode model for electrical impedance tomography and show that current-to-voltage measurements from finitely many electrodes are sufficient to characterize the positions of a finite number of point-like inclusions. More precisely, we consider an asymptotic expansion with respect to the size of the small inclusions of the relative Neumann-to-Dirichlet operator in the framework of the point electrode model. This operator is naturally finite-dimensional and models difference measurements by finitely many small electrodes of the electric potential with and without the small inclusions. Moreover, its leading-order term explicitly characterizes the centers of the small inclusions if the (finite) number of point electrodes is large enough. This characterization is based on finite-dimensional test vectors and leads naturally to a MUSIC algorithm for imaging the inclusion centers. We show both the feasibility and limitations of this imaging technique via two-dimensional numerical experiments, considering in particular the influence of the number of point electrodes on the algorithm's images.