Table of Contents Author Guidelines Submit a Manuscript
International Journal of Antennas and Propagation
Volume 2019, Article ID 9014969, 12 pages
https://doi.org/10.1155/2019/9014969
Research Article

A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging

1Electrical Engineering Department, Chalmers University of Technology, 41296 Gothenburg, Sweden
2The Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA

Correspondence should be addressed to Samar Hosseinzadegan; es.sremlahc@hramas

Received 26 February 2019; Revised 6 May 2019; Accepted 20 May 2019; Published 17 July 2019

Guest Editor: Sandra Costanzo

Copyright © 2019 Samar Hosseinzadegan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. J. Brenner and E. J. Hall, “Computed tomography—an increasing source of radiation exposure,” The New England Journal of Medicine, vol. 357, no. 22, pp. 2277–2284, 2007. View at Publisher · View at Google Scholar · View at Scopus
  2. T. Jansson, J. E. Westlin, H. Ahlström, A. Lilja, B. Långström, and J. Bergh, “Positron emission tomography studies in patients with locally advanced and/or metastatic breast cancer: a method for early therapy evaluation?” Journal of Clinical Oncology, vol. 13, no. 6, pp. 1470–1477, 1995. View at Publisher · View at Google Scholar
  3. D. M. Ikeda, D. R. Baker, and B. L. Daniel, “Magnetic resonance imaging of breast cancer: Clinical indications and breast MRI reporting system,” Journal of Magnetic Resonance Imaging, vol. 12, no. 6, pp. 975–983, 2000. View at Publisher · View at Google Scholar · View at Scopus
  4. S. G. Orel and M. D. Schnall, “MR imaging of the breast for the detection, diagnosis, and staging of breast cancer,” Radiology, vol. 220, no. 1, pp. 13–30, 2001. View at Publisher · View at Google Scholar · View at Scopus
  5. E. Porter, M. Coates, and M. Popović, “An early clinical study of time-domain microwave radar for breast health monitoring,” IEEE Transactions on Biomedical Engineering, vol. 63, no. 3, pp. 530–539, 2016. View at Publisher · View at Google Scholar · View at Scopus
  6. E. C. Fear, J. Bourqui, C. Curtis, D. Mew, B. Docktor, and C. Romano, “Microwave breast imaging with a monostatic radar-based system: a study of application to patients,” IEEE Transactions on Microwave Theory and Techniques, vol. 61, no. 5, pp. 2119–2128, 2013. View at Publisher · View at Google Scholar · View at Scopus
  7. A. W. Preece, I. Craddock, M. Shere, L. Jones, and H. L. Winton, “MARIA M4: Clinical evaluation of a prototype ultrawideband radar scanner for breast cancer detection,” Journal of Medical Imaging, vol. 3, no. 3, Article ID 033502, 2016. View at Google Scholar · View at Scopus
  8. H. Song, S. Sasada, T. Kadoya et al., “Detectability of breast tumor by a hand-held impulse-radar detector: performance evaluation and pilot clinical study,” Scientific Reports, vol. 7, Article ID 16353, 2017. View at Google Scholar
  9. R. K. Amineh, M. Ravan, A. Khalatpour, and N. K. Nikolova, “Three-dimensional near-field microwave holography using reflected and transmitted signals,” IEEE Transactions on Antennas and Propagation, vol. 59, no. 12, pp. 4777–4789, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Tajik, F. Foroutan, D. S. Shumakov, A. D. Pitcher, and N. K. Nikolova, “Real-time microwave imaging of a compressed breast phantom with planar scanning,” IEEE Journal of Electromagnetics, RF and Microwaves in Medicine and Biology, vol. 2, pp. 154–162, 2018. View at Google Scholar
  11. R. A. Kruger, D. R. Reinecke, and G. A. Kruger, “Thermoacoustic computed tomography–technical considerations,” Medical Physics, vol. 26, no. 9, pp. 1832–1837, 1999. View at Publisher · View at Google Scholar · View at Scopus
  12. G. Ku and L. V. Wang, “Scanning microwave-induced thermoacoustic tomography: signal, resolution, and contrast,” Medical physics, vol. 28, pp. 4–10, 2001. View at Google Scholar
  13. S. P. Poplack, T. D. Tosteson, W. A. Wells et al., “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology, vol. 243, no. 2, pp. 350–359, 2007. View at Publisher · View at Google Scholar
  14. P. M. Meaney, P. A. Kaufman, L. S. Muffly et al., “Microwave imaging for neoadjuvant chemotherapy monitoring: initial clinical experience,” Breast Cancer Research, vol. 15, article R35, 2013. View at Google Scholar
  15. S. Y. Semenov, A. E. Bulyshev, A. Abubakar et al., “Microwave-tomographic imaging of the high dielectric-contrast objects using different image-reconstruction approaches,” IEEE Transactions on Microwave Theory and Techniques, vol. 53, no. 7, pp. 2284–2294, 2005. View at Publisher · View at Google Scholar · View at Scopus
  16. J. D. Shea, P. Kosmas, S. C. Hagness, and B. D. Van Veen, “Three-dimensional microwave imaging of realistic numerical breast phantoms via a multiple-frequency inverse scattering technique,” Medical Physics, vol. 37, no. 8, pp. 4210–4226, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. P. Tournier, M. Bonazzoli, V. Dolean et al., “Numerical modeling and high-speed parallel computing: new perspectives on tomographic microwave imaging for brain stroke detection and monitoring,” IEEE Antennas and Propagation Magazine, vol. 59, no. 5, pp. 98–110, 2017. View at Publisher · View at Google Scholar
  18. O. M. Bucci, L. Crocco, and R. Scapaticci, “On the optimal measurement configuration for magnetic nanoparticles-enhanced breast cancer microwave imaging,” IEEE Transactions on Biomedical Engineering, vol. 62, no. 2, pp. 407–414, 2015. View at Publisher · View at Google Scholar · View at Scopus
  19. Z. Miao and P. Kosmas, “Multiple-frequency DBIM-TwIST algorithm for microwave breast imaging,” IEEE Transactions on Antennas and Propagation, vol. 65, no. 5, pp. 2507–2516, 2017. View at Publisher · View at Google Scholar · View at Scopus
  20. I. Catapano, L. Crocco, M. D' Urso, and T. Isernia, “3D microwave imaging via preliminary support reconstruction: testing on the Fresnel 2008 database,” Inverse Problems, vol. 25, no. 2, Article ID 024002, 23 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. A. Fasoula, L. Duchesne, J. Gil Cano, P. Lawrence, G. Robin, and J. Bernard, “On-site validation of a microwave breast imaging system, before first patient study,” Diagnostics, vol. 8, no. 3, article 53, 2018. View at Publisher · View at Google Scholar
  22. R. Scapaticci, P. Kosmas, and L. Crocco, “Wavelet-based regularization for robust microwave imaging in medical applications,” IEEE Transactions on Biomedical Engineering, vol. 62, no. 4, pp. 1195–1202, 2015. View at Publisher · View at Google Scholar · View at Scopus
  23. T. Rydholm, A. Fhager, M. Persson, and P. M. Meaney, “A first evaluation of the realistic supelec-breast phantom,” IEEE Journal of Electromagnetics, RF and Microwaves in Medicine and Biology, vol. 1, pp. 59–65, 2017. View at Google Scholar
  24. T. Rydholm, A. Fhager, M. Persson, S. Geimer, and P. Meaney, “Effects of the plastic of the realistic GeePS-L2S-breast phantom,” Diagnostics, vol. 8, article 61, 2018. View at Publisher · View at Google Scholar
  25. P. M. Meaney, M. W. Fanning, T. Raynolds et al., “Initial clinical experience with microwave breast imaging in women with normal mammography,” Academic Radiology, vol. 14, no. 2, pp. 207–218, 2007. View at Publisher · View at Google Scholar · View at Scopus
  26. P. M. Meaney, M. W. Fanning, D. Li, S. P. Poplack, and K. D. Paulsen, “A clinical prototype for active microwave imaging of the breast,” IEEE Transactions on Microwave Theory and Techniques, vol. 48, no. 1, pp. 1841–1853, 2000. View at Publisher · View at Google Scholar · View at Scopus
  27. S. Semenov, R. Svenson, A. Boulyshev et al., “Microwave tomography: two-dimensional system for biological imaging,” IEEE Transactions on Biomedical Engineering, vol. 43, no. 9, pp. 869–877, 1996. View at Publisher · View at Google Scholar
  28. P. M. Meaney, F. Shubitidze, M. W. Fanning et al., “Surface wave multipath signals in near-field microwave imaging,” Journal of Biomedical Imaging, vol. 2012, Article ID 697253, 8 pages, 2012. View at Google Scholar
  29. Q. Fang, P. M. Meaney, and K. D. Paulsen, “Singular value analysis of the Jacobian matrix in microwave image reconstruction,” IEEE Transactions on Antennas and Propagation, vol. 54, no. 8, pp. 2371–2380, 2006. View at Publisher · View at Google Scholar · View at Scopus
  30. P. M. Meaney, Q. Fang, T. Rubaek, E. Demidenko, and K. D. Paulsen, “Log transformation benefits parameter estimation in microwave tomographic imaging,” Medical Physics, vol. 34, no. 6, pp. 2014–2023, 2007. View at Publisher · View at Google Scholar · View at Scopus
  31. P. M. Meaney, S. D. Geimer, and K. D. Paulsen, “Two-step inversion in microwave imaging with a logarithmic transformation,” Medical Physics, vol. 44, no. 8, pp. 4239–4251, 2017. View at Publisher · View at Google Scholar · View at Scopus
  32. A. Fhager, M. Gustafsson, and S. Nordebo, “Image reconstruction in microwave tomography using a dielectric debye model,” IEEE Transactions on Biomedical Engineering, vol. 59, no. 1, pp. 156–166, 2012. View at Publisher · View at Google Scholar · View at Scopus
  33. Q. Fang, P. M. Meaney, and K. D. Paulsen, “Viable three-dimensional medical microwave tomography: theory and numerical experiments,” IEEE Transactions on Antennas and Propagation, vol. 58, no. 2, pp. 449–458, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, “Evolutionary optimization as applied to inverse scattering problems,” Inverse Problems, vol. 25, no. 12, Article ID 123003, 2009. View at Google Scholar · View at Scopus
  35. T. M. Grzegorczyk, P. M. Meaney, P. A. Kaufman, R. M. Diflorio-Alexander, and K. D. Paulsen, “Fast 3-D tomographic microwave imaging for breast cancer detection,” IEEE Transactions on Medical Imaging, vol. 31, no. 8, pp. 1584–1592, 2012. View at Publisher · View at Google Scholar · View at Scopus
  36. S. Hosseinzadegan, A. Fhager, M. Persson, and P. Meaney, “Application of two-dimensional discrete dipole approximation in simulating electric field of a microwave breast imaging system,” IEEE Journal of Electromagnetics, RF and Microwaves in Medicine and Biology, 2018. View at Google Scholar
  37. M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” in Proceedings of the IEEE Special Issue on Program Generation, Optimization, and Platform Adaptation, vol. 93, pp. 216–231, 2005.
  38. E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” The Astrophysical Journal, vol. 186, pp. 705–714, 1973. View at Publisher · View at Google Scholar
  39. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” Journal of the Optical Society of America A, vol. 11, pp. 1491–1499, 1994. View at Google Scholar
  40. K. Skorupski, “Using the DDA (discrete dipole approximation) method in determining the extinction cross section of black carbon,” Metrology and Measurement Systems, vol. 22, no. 1, pp. 153–164, 2015. View at Publisher · View at Google Scholar
  41. A. Lakhtakia, “Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields,” International Journal of Modern Physics C, vol. 3, pp. 583–603, 1992. View at Publisher · View at Google Scholar
  42. W. C. Chew, Waves and Fields in Inhomogeneous Media, IEEE press, 1995.
  43. B. T. Draine and J. Goodman, “Beyond clausius-mossotti-wave propagation on a polarizable point lattice and the discrete dipole approximation,” The Astrophysical Journal, vol. 405, no. 2, pp. 685–697, 1993. View at Publisher · View at Google Scholar · View at Scopus
  44. F. Kahnert, “Numerical methods in electromagnetic scattering theory,” Journal of Quantitative Spectroscopy & Radiative Transfer, vol. 79-80, pp. 775–824, 2003. View at Publisher · View at Google Scholar
  45. M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “Convergence of the discrete dipole approximation. I. theoretical analysis,” The Journal of the Optical Society of America A (JOSA A), vol. 23, pp. 2578–2591, 2006. View at Publisher · View at Google Scholar
  46. A. Sihvola, “Peculiarities in the dielectric response of negative-permittivity scatterers,” Progress in Electromagnetics Research, vol. 66, pp. 191–198, 2006. View at Publisher · View at Google Scholar · View at Scopus
  47. G. H. Golub and C. F. Van Loan, Matrix Computations, vol. 3, JHU Press, 2012.
  48. P. J. Flatau, “Improvements in the discrete-dipole approximation method of computing scattering and absorption,” Optics Expresss, vol. 22, no. 16, p. 1205, 1997. View at Publisher · View at Google Scholar
  49. J. J. Goodman, P. J. Flatau, and B. T. Draine, “Application of fast-Fourier-transform techniques to the discrete-dipole approximation,” Optics Expresss, vol. 16, no. 15, pp. 1198–1200, 1991. View at Publisher · View at Google Scholar · View at Scopus
  50. P. Sonneveld, “CGS, a fast lanczos-type solver for nonsymmetric linear systems,” SIAM Journal on Scientific and Statistical Computing, vol. 10, no. 1, pp. 36–52, 1989. View at Publisher · View at Google Scholar
  51. H. A. van der Vorst, “BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems,” SIAM Journal on Scientific and Statistical Computing, vol. 13, no. 2, pp. 631–644, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  52. M. H. Gutknecht, “Variants of BICGSTAB for matrices with complex spectrum,” SIAM Journal on Scientific Computing, vol. 14, no. 5, pp. 1020–1033, 1993. View at Publisher · View at Google Scholar
  53. Y. Saad and M. Schultz, “GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM Journal on Scientific and Statistical Computing, vol. 7, no. 3, pp. 856–869, 1986. View at Publisher · View at Google Scholar
  54. R. W. Freund, “A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems,” SIAM Journal on Scientific Computing, vol. 14, no. 2, pp. 470–482, 1993. View at Publisher · View at Google Scholar
  55. R. W. Freund, “Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices,” SIAM Journal on Scientific and Statistical Computing, vol. 13, no. 1, pp. 425–448, 1992. View at Publisher · View at Google Scholar
  56. M. Clemens and T. Weiland, “Iterative methods for the solution of very large complex symmetric linear systems of equations in electrodynamics,” Front Range Scientific Computations, Inc, Lakewood, NJ, USA, 1996. View at Google Scholar
  57. H. A. van der Vorst and J. B. M. Melissen, “Petrov-Galerkin type method for solving Ax = b, where A is symmetric complex,” IEEE Transactions on Magnetics, vol. 26, no. 2, pp. 706–708, 1990. View at Publisher · View at Google Scholar · View at Scopus
  58. T. Sogabe and S.-L. Zhang, “A COCR method for solving complex symmetric linear systems,” Journal of Computational and Applied Mathematics, vol. 199, no. 2, pp. 297–303, 2007. View at Publisher · View at Google Scholar · View at Scopus
  59. C. Sanderson and R. Curtin, “Armadillo: a template-based C++ library for linear algebra,” Journal of Open Source Software, 2016. View at Google Scholar
  60. C. Sanderson and R Curtin, “A user-friendly hybrid sparse matrix class in C++,” in Proceedings of the International Congress on Mathematical Software, pp. 422–430, 2018.
  61. S. Hosseinzadegan, A discrete dipole approximation forward solver for microwave breast imaging [Dissertation, thesis], Chalmers University of Technology, 2019.