Microwave Tomography Using Topology Optimization Techniques

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.

[1]  J. Petersson,et al.  Topology optimization using regularized intermediate density control , 2001 .

[2]  E. Wadbro,et al.  Topology optimization of an acoustic horn , 2006 .

[3]  D. Dobson.  Optimal Mode Coupling in Simple Planar Waveguides , 2006 .

[4]  E. Haber,et al.  Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach , 2004 .

[5]  W. Joines,et al.  The measured electrical properties of normal and malignant human tissues from 50 to 900 MHz. , 1994, Medical physics.

[6]  Robert H. Svenson,et al.  Microwave tomography: theoretical and experimental investigation of the iteration reconstruction algorithm , 1998 .

[7]  Robert H. Svenson,et al.  Microwave Spectroscopy of Myocardial Ischemia and Infarction. 2. Biophysical Reconstruction , 2004, Annals of Biomedical Engineering.

[8]  C. Pichot,et al.  Inverse scattering: an iterative numerical method for electromagnetic imaging , 1991 .

[9]  P.M. van den Berg,et al.  Microwave-tomographic imaging of the high dielectric-contrast objects using different image-reconstruction approaches , 2005, IEEE Transactions on Microwave Theory and Techniques.

[10]  P.M. Meaney,et al.  Microwave imaging for tissue assessment: initial evaluation in multitarget tissue-equivalent phantoms , 1996, IEEE Transactions on Biomedical Engineering.

[11]  R. Kohn,et al.  Topology optimization and optimal shape design using homogenization , 1993 .

[12]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[13]  Avinash C. Kak,et al.  Principles of computerized tomographic imaging , 2001, Classics in applied mathematics.

[14]  Martin P. Bendsøe.  Topology Optimization , 2009, Encyclopedia of Optimization.

[15]  Robert H. Svenson,et al.  Microwave tomography: a two-dimensional Newton iterative scheme , 1998 .

[16]  Eddie Wadbro,et al.  Topology optimization of wave transducers , 2006 .

[17]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[18]  J. Petersson,et al.  Topology optimization of fluids in Stokes flow , 2003 .

[19]  Gregory A. Newman,et al.  Solution strategies for two- and three-dimensional electromagnetic inverse problems , 2000 .

[20]  P. Grisvard.  Elliptic Problems in Nonsmooth Domains , 1985 .

[21]  O. Dorn,et al.  Level set methods for inverse scattering , 2006 .

[22]  Steven J. Cox,et al.  Maximizing Band Gaps in Two-Dimensional Photonic Crystals , 1999, SIAM J. Appl. Math..

[23]  Weng Cho Chew,et al.  Nonlinear diffraction tomography-the use of inverse scattering for imaging , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[24]  Robert H. Svenson,et al.  Microwave Spectroscopy of Myocardial Ischemia and Infarction. 1. Experimental Study , 2004, Annals of Biomedical Engineering.