Microwave tomography using topology optimization techniques
2008 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 30, no 3, 1613-1633 p.Article in journal (Refereed) Published
Microwave tomography is a technique in which microwaves illuminate a specimen, and measurements of the scattered electrical field are used to determine and depict the specimen's dielectric and conductive properties. This article presents a new method to perform the reconstruction. The reconstruction method is illustrated by assuming time harmonic scattering in two space dimensions in a setup tailored for medical applications. We prove that the resulting constrained nonlinear least-squares problem admits a solution. The governing Helmholtz equation is discretized by using the finite-element method, and the dielectric properties are allowed to attain different values at each element within a given region. The reconstruction algorithm uses methodologies borrowed from topology optimization of linearly elastic structures. Numerical examples illustrate the reconstruction method in a parameter range typical for human tissue and for the challenging case where the size of the object is in the same order as the wavelength. A reasonable estimate of the dielectric properties is obtained by using one observation per 20 unknowns when the permittivity is allowed to vary continuously within a given interval. Using a priori information that the permittivity attains only certain values results in a good estimate and a sharp image. As opposed to topology optimization for structures, there is no indication of mesh dependency and checkerboarding when forcing the permittivity to attain discrete values.
Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics , 2008. Vol. 30, no 3, 1613-1633 p.
microwave tomography, topology optimization, inverse problems, Maxwell equations, Helmholtz equation
IdentifiersURN: urn:nbn:se:umu:diva-40288DOI: 10.1137/070679879OAI: oai:DiVA.org:umu-40288DiVA: diva2:399145