A Shape-Based Inversion Algorithm Applied to Microwave Imaging of Breast Tumors

We propose a new shape-based inversion algorithm to identify an anomaly embedded in an inhomogeneous layered geometry. We apply our approach to microwave breast imaging where the geometry consists of several inhomogeneous layers and the potential tumor is embedded in the innermost layer. In addition to the tumor identification, we estimate the irregular transition layer between the breast inner layers. Our inversion algorithm is based on a low-dimensional parametric form of the relevant geometries, and uses multiple-frequency multi-source data to estimate the unknowns. Several numerical examples are provided to evaluate the effectiveness of our approach and demonstrate its robustness both to the initial choice of parameter values and uncertainty in the complex dielectric properties of the media even with the complex geometry and the simplified inverse model.

[1]  X. Li,et al.  Confocal microwave imaging for breast cancer detection: localization of tumors in three dimensions , 2002, IEEE Transactions on Biomedical Engineering.

[2]  H.D. Ramadan,et al.  Confocal Microwave Imaging for Breast Cancer Detection Via Adaptive Beamforming , 2007, 2007 National Radio Science Conference.

[3]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[4]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[5]  Om P. Gandhi,et al.  A frequency-dependent finite-difference time-domain formulation for general dispersive media , 1993 .

[6]  Qing Huo Liu,et al.  Three-dimensional nonlinear image reconstruction for microwave biomedical imaging , 2004, IEEE Transactions on Biomedical Engineering.

[7]  George Robinson,et al.  The Calculus of Observations - A Treatise on Numerical Mathematics , 1924 .

[8]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[9]  W. Marsden.  I and J , 2012 .

[10]  Earl Zastrow,et al.  3D computational study of non-invasive patient-specific microwave hyperthermia treatment of breast cancer , 2010, Physics in medicine and biology.

[11]  Dana H. Brooks,et al.  Electrical Impedance Tomography for Piecewise Constant Domains Using Boundary Element Shape-Based Inverse Solutions , 2007, IEEE Transactions on Medical Imaging.

[12]  R. B. Standler,et al.  A frequency-dependent finite-difference time-domain formulation for dispersive materials , 1990 .

[13]  R. W. Lau,et al.  The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. , 1996, Physics in medicine and biology.

[14]  Dennis M. Sullivan,et al.  Z-transform theory and the FDTD method , 1996 .

[15]  Robert H. Svenson,et al.  Computational modeling of three-dimensional microwave tomography of breast cancer , 2001, IEEE Transactions on Biomedical Engineering.

[16]  Aria Abubakar,et al.  Inversion of controlled‐source electromagnetic data using a model‐based approach , 2010 .

[17]  Francis A. Duck,et al.  Physical properties of tissue : a comprehensive reference book , 1990 .

[18]  S. S. Chaudhary,et al.  Dielectric properties of normal & malignant human breast tissues at radiowave & microwave frequencies. , 1984, Indian journal of biochemistry & biophysics.

[19]  C. D. Boor,et al.  On Calculating B-splines , 1972 .

[20]  J. D. Shea,et al.  Three-dimensional microwave imaging of realistic numerical breast phantoms via a multiple-frequency inverse scattering technique. , 2010, Medical physics.

[21]  R. W. Lau,et al.  The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. , 1996, Physics in medicine and biology.

[22]  A. Taflove,et al.  Two-dimensional FDTD analysis of a pulsed microwave confocal system for breast cancer detection: fixed-focus and antenna-array sensors , 1998, IEEE Transactions on Biomedical Engineering.

[23]  C. Hines.  Electromagnetic Waves , 2021, Nature.

[24]  W. Clem Karl,et al.  Reconstructing Ellipsoids from Projections , 1994, CVGIP Graph. Model. Image Process..

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

[26]  Tejas Mehta,et al.  Current uses of ultrasound in the evaluation of the breast. , 2003, Radiologic clinics of North America.

[27]  Stuchly,et al.  DIELECTRIC PROPERTIES OF BIOLOGICAL SUBSTANCES–TABULATED , 1980 .

[28]  S. Heywang-Köbrunner,et al.  Contrast-Enhanced MRI of the Breast , 1991 .

[29]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[30]  Eric L. Miller,et al.  Optimum PML ABC conductivity profile in FDFD , 1999 .

[31]  Wesley E. Snyder,et al.  Application of Affine-Invariant Fourier Descriptors to Recognition of 3-D Objects , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[32]  Zhong Qing Zhang,et al.  Active microwave imaging. I. 2-D forward and inverse scattering methods , 2002 .

[33]  C Gabriel,et al.  The dielectric properties of biological tissues: I. Literature survey. , 1996, Physics in medicine and biology.

[34]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[35]  K. Paulsen,et al.  IMPORTANCE OF USING A REDUCED CONTRAST COUPLING MEDIUM IN 2D MICROWAVE BREAST IMAGING , 2003 .

[36]  C. D. Boor,et al.  On Calculating with B-Splines II. Integration , 1976 .

[37]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[38]  Paul M. Meaney,et al.  Conformal microwave imaging for breast cancer detection , 2003 .

[39]  M. Lindstrom,et al.  A large-scale study of the ultrawideband microwave dielectric properties of normal breast tissue obtained from reduction surgeries , 2007, Physics in medicine and biology.

[40]  David Boas,et al.  Three-dimensional shape-based imaging of absorption perturbation for diffuse optical tomography. , 2003, Applied optics.

[41]  D. Land,et al.  Dielectric properties of female human breast tissue measured in vitro at 3.2 GHz. , 1992, Physics in medicine and biology.

[42]  Larry L. Schumaker,et al.  Spline functions - basic theory, Third Edition , 2007, Cambridge mathematical library.

[43]  J Ryan,et al.  Mammographic screening for breast cancer. , 2003, The New England journal of medicine.

[44]  J. D. Shea,et al.  Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms , 2010, Inverse problems.

[45]  A. Taflove,et al.  Three-dimensional FDTD analysis of a pulsed microwave confocal system for breast cancer detection: design of an antenna-array element , 1999 .

[46]  Qing Huo Liu,et al.  Microwave breast imaging: 3-D forward scattering simulation , 2003, IEEE Transactions on Biomedical Engineering.

[47]  E. Fear.  Microwave Imaging of the Breast , 2005, Technology in cancer research & treatment.

[48]  Paul M. Meaney,et al.  A clinical prototype for active microwave imaging of the breast , 2000 .

[49]  Carl Tim Kelley,et al.  Iterative methods for optimization , 1999, Frontiers in applied mathematics.

[50]  Sh. Heywang Kobrunner.  Contrast-enhanced magnetic resonance imaging of the breast , 1994 .

[51]  R. Pethig.  Dielectric Properties of Biological Materials: Biophysical and Medical Applications , 1984, IEEE Transactions on Electrical Insulation.

[52]  Robert H. Svenson,et al.  Two-dimensional computer analysis of a microwave flat antenna array for breast cancer tomography , 2000 .

[53]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[54]  Stuchly,et al.  Dielectric properties of breast carcinoma and the surrounding tissues , 1988, IEEE Transactions on Biomedical Engineering.