A shape optimization approach for electrical impedance tomography with point measurements

Author(s)

Albuquerque, Yuri Flores ; Laurain, Antoine ; Sturm, Kevin

• Document type: Journal article
• Source: INVERSE PROBLEMS; v. 36, n. 9, p. 27-pg., 2020-09-01.

Abstract

Working within the class of piecewise constant conductivities, the inverse problem of electrical impedance tomography can be recast as a shape optimization problem where the discontinuity interface is the unknown. Using Groger'sWp1<i-estimates for mixed boundary value problems, the averaged adjoint method is extended to the case of Banach spaces, which allows one to compute the derivative of shape functionals involving point evaluations. We compute the corresponding distributed expression of the shape derivative and show that it may contain Dirac measures in addition to the usual domain integrals. We use this distributed shape derivative to devise a numerical algorithm, show various numerical results supporting the method, and based on these results we discuss the influence of the point measurements patterns on the quality of the reconstructions. (AU)

• FAPESP's process: 14/50279-4 - Brasil Research Centre for Gas Innovation
• Grantee: Julio Romano Meneghini
• Support Opportunities: Research Grants - Research Centers in Engineering Program
• FAPESP's process: 16/24776-6 - Shape optimization and free boundary problems
• Grantee: Antoine Laurain
• Support Opportunities: Regular Research Grants