Comparison of an Enhanced Distorted Born Iterative Method and the Multiplicative-Regularized Contrast Source Inversion method

For 2D transverse magnetic (TM) microwave inversion, multiplicative-regularized contrast source inversion (MR-CSI), and the distorted Born iterative method (DBIM) are compared. The comparison is based on a computational resource analysis, inversion of synthetic data, and inversion of experimentally collected data from both the Fresnel and UPC Barcelona data sets. All inversion results are blind, but appropriate physical values for the reconstructed contrast are maintained. The data sets used to test the algorithms vary widely in terms of the background media, antennas, and far/near field considerations. To ensure that the comparison is replicable, an automatic regularization parameter selection method is used for the additive regularization within the DBIM, which utilizes a fast implementation of the L-curve method and the Laplacian regularizer. While not used in the classical DBIM, we introduce an MR term to the DBIM in order to provide comparable results to MR-CSI. The introduction of this MR term requires only slight modifications to the classical DBIM algorithm, and adds little computational complexity. The results show that with the addition of the MR term in the DBIM, the two algorithms provide very similar inversion results, but with the MR-CSI method providing advantages for both computational resources and ease of implementation.

[1]  Aria Abubakar,et al.  A multiplicative regularization approach for deblurring problems , 2004, IEEE Transactions on Image Processing.

[2]  E.C. Fear,et al.  Tissue Sensing Adaptive Radar for Breast Cancer Detection—Experimental Investigation of Simple Tumor Models , 2005, IEEE Transactions on Microwave Theory and Techniques.

[3]  P. M. Berg,et al.  A modified gradient method for two-dimensional problems in tomography , 1992 .

[4]  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.

[5]  A. N. Tikhonov,et al.  REGULARIZATION OF INCORRECTLY POSED PROBLEMS , 1963 .

[6]  P. M. van den Berg,et al.  TWO- AND THREE-DIMENSIONAL ALGORITHMS FOR MICROWAVE IMAGING AND INVERSE SCATTERING , 2003 .

[7]  Aria Abubakar,et al.  2.5D forward and inverse modeling for interpreting low-frequency electromagnetic measurements , 2008 .

[8]  P. M. Berg,et al.  The three dimensional weak form of the conjugate gradient FFT method for solving scattering problems , 1992 .

[9]  Jordi J. Mallorquí,et al.  Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography , 1998, IEEE Transactions on Medical Imaging.

[10]  Gene H. Golub,et al.  Generalized cross-validation as a method for choosing a good ridge parameter , 1979, Milestones in Matrix Computation.

[11]  Robert H. Svenson,et al.  Dielectrical spectroscopy of canine myocardium during acute ischemia and hypoxia at frequency spectrum from 100 kHz to 6 GHz , 2002, IEEE Transactions on Medical Imaging.

[12]  P. M. van den Berg,et al.  On the equivalence of the Newton-Kantorovich and distorted Born methods , 2000 .

[13]  O. Nelles,et al.  An Introduction to Optimization , 1996, IEEE Antennas and Propagation Magazine.

[14]  C. Eyraud,et al.  Free space experimental scattering database continuation: experimental set-up and measurement precision , 2005 .

[15]  P. M. Berg,et al.  Imaging of biomedical data using a multiplicative regularized contrast source inversion method , 2002 .

[16]  W. Chew,et al.  A frequency-hopping approach for microwave imaging of large inhomogeneous bodies , 1995, IEEE Antennas and Propagation Society International Symposium. 1995 Digest.

[17]  Xu Li,et al.  Microwave imaging via space-time beamforming for early detection of breast cancer , 2003 .

[18]  David Wall,et al.  On Frechet differentiability of some nonlinear operators occurring in inverse problems: an implicit function theorem approach , 1990 .

[19]  J. Richmond.  Scattering by a dielectric cylinder of arbitrary cross section shape , 1965 .

[20]  K. Paulsen,et al.  Nonlinear Microwave Imaging for Breast-Cancer Screening Using Gauss–Newton's Method and the CGLS Inversion Algorithm , 2007, IEEE Transactions on Antennas and Propagation.

[21]  Dianne P. O'Leary,et al.  The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems , 1993, SIAM J. Sci. Comput..

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

[23]  P. M. Berg,et al.  Iterative forward and inverse algorithms based on domain integral equations for three-dimensional electric and magnetic objects , 2004 .

[24]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[25]  P. Hansen,et al.  Exploiting Residual Information in the Parameter Choice for Discrete Ill-Posed Problems , 2006 .

[26]  Per Christian Hansen,et al.  L-Curve Curvature Bounds via Lanczos Bidiagonalization , 2001 .

[27]  P. M. Berg,et al.  A contrast source inversion method , 1997 .

[28]  N. Joachimowicz,et al.  Database of "In Vivo" Measurements for Quantitative Microwave Imaging and Reconstruction Algorithms , 1995, IEEE Antennas and Propagation Magazine.

[29]  Matteo Pastorino,et al.  A computational technique based on a real-coded genetic algorithm for microwave imaging purposes , 2000, IEEE Trans. Geosci. Remote. Sens..

[30]  W. Chew,et al.  Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method. , 1990, IEEE transactions on medical imaging.

[31]  Aria Abubakar,et al.  Application of the multiplicative regularized contrast source inversion method on TM- and TE-polarized experimental Fresnel data , 2005 .

[32]  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.

[33]  Aria Abubakar,et al.  Inversion of experimental multi-frequency data using the contrast source inversion method , 2001 .

[34]  V. A. Morozov,et al.  Methods for Solving Incorrectly Posed Problems , 1984 .

[35]  J. Lovetri,et al.  Preliminary Investigation of the NCP Parameter-Choice Method for Inverse Scattering Problems Using BIM: 2-D TM Case , 2008 .

[36]  A. Franchois,et al.  Full-Wave Three-Dimensional Microwave Imaging With a Regularized Gauss–Newton Method— Theory and Experiment , 2007, IEEE Transactions on Antennas and Propagation.

[37]  Anton G. Tijhuis,et al.  Transient scattering by a lossy dielectric cylinder: marching-on-in-frequency approach , 1993 .

[38]  P. M. van den Berg,et al.  Total variation as a multiplicative constraint for solving inverse problems. , 2001, IEEE transactions on image processing : a publication of the IEEE Signal Processing Society.

[39]  P. Kosmas,et al.  FDTD-based time reversal for microwave breast cancer Detection-localization in three dimensions , 2006, IEEE Transactions on Microwave Theory and Techniques.

[40]  P. Hansen.  Numerical tools for analysis and solution of Fredholm integral equations of the first kind , 1992 .