Three-dimensional quantitative microwave imaging from measured data with multiplicative smoothing and value picking regularization

This paper presents reconstructions of four targets from the 3D Fresnel database. The electromagnetic inverse scattering problem is treated as a nonlinear optimization problem for the complex permittivity in an investigation domain. The goal of this paper is to explore the achievable reconstruction quality when such a quantitative inverse scattering approach is employed on real world measurements, using only single-frequency data. Two regularization techniques to reduce the ill-possedness of the inverse scattering problem are compared. The first one is a multiplicative smoothing regularization, applied directly to the cost function, which yields smoothed reconstructions of the homogeneous Fresnel targets without much experimentation to determine the regularization parameter. The second technique is the recently proposed value picking (VP) regularization which is particularly suited for the class of piecewise (quasi-)homogeneous targets, such as those of the Fresnel database. In contrast to edge-preserving regularization methods, VP regularization does not operate on the spatial distribution of permittivity values, but it clusters them around some reference values, the VP values, in the complex plane. These VP values are included in the cost function as auxiliary optimization variables and their number can be gradually increased using a stepwise relaxed VP regularization scheme. Both regularization strategies are incorporated in a Gauss–Newton minimization framework with line search. It is shown that the reconstruction quality using single-frequency Fresnel data is good when using multiplicative smoothing and even better when using the VP regularization. In particular, the completely blind reconstruction of the mystery target in the database provides us with a detailed quantitative image of a plausible object.

[1]  Robert H. Svenson,et al.  Three-dimensional microwave tomography. Theory and computer experiments in scalar approximation , 2000 .

[2]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[3]  Michel Barlaud,et al.  Microwave imaging: Reconstructions from experimental data using conjugate gradient and enhancement by edge‐preserving regularization , 1997 .

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

[5]  C. Pichot,et al.  Microwave imaging-complex permittivity reconstruction with a Levenberg-Marquardt method , 1997 .

[6]  Jean-Paul Hugonin,et al.  Microwave imaging-complex permittivity reconstruction-by simulated annealing , 1991 .

[7]  AG Anton Tijhuis,et al.  A quasi‐Newton reconstruction algorithm for a complex microwave imaging scanner environment , 2003 .

[8]  F. Santosa,et al.  Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set , 1998 .

[9]  Michel Barlaud,et al.  Deterministic edge-preserving regularization in computed imaging , 1997, IEEE Trans. Image Process..

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

[11]  P. Hansen,et al.  Subspace Preconditioned LSQR for Discrete Ill-Posed Problems , 2003 .

[12]  P. M. Berg,et al.  The diagonalized contrast source approach: an inversion method beyond the Born approximation , 2005 .

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

[14]  Pierre Sabouroux,et al.  Continuing with the Fresnel database: experimental setup and improvements in 3D scattering measurements , 2009 .

[15]  J. D. Zaeytijd.  On the 3D electromagnetic quantitative inverse scattering problem: algorithms and regularization , 2009 .

[16]  Andrea Massa,et al.  Full-vectorial three-dimensional microwave imaging through the iterative multiscaling strategy-a preliminary assessment , 2005, IEEE Geoscience and Remote Sensing Letters.

[17]  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.

[18]  A. Franchois,et al.  A New Value Picking Regularization Strategy—Application to the 3-D Electromagnetic Inverse Scattering Problem , 2009, IEEE Transactions on Antennas and Propagation.

[19]  Lorenzo Crocco,et al.  A novel effective model for solving 3-D nonlinear inverse scattering problems in lossy scenarios , 2006, IEEE Geoscience and Remote Sensing Letters.

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

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

[22]  A. Abubakar,et al.  A General Framework for Constraint Minimization for the Inversion of Electromagnetic Measurements , 2004 .

[23]  T. Isernia,et al.  Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

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

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

[26]  Anne Sentenac,et al.  Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[27]  Aria Abubakar,et al.  The contrast source inversion method for location and shape reconstructions , 2002 .

[28]  Amélie Litman,et al.  Theoretical and computational aspects of 2-D inverse profiling , 2001, IEEE Trans. Geosci. Remote. Sens..

[29]  Michel Barlaud,et al.  Conjugate-gradient algorithm with edge-preserving regularization for image reconstruction from Ipswi , 1997 .

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

[31]  T. Isernia,et al.  Inverse scattering with real data: detecting and imaging homogeneous dielectric objects , 2001 .

[32]  Steven G. Johnson,et al.  The Design and Implementation of FFTW3 , 2005, Proceedings of the IEEE.

[33]  Lorenzo Crocco,et al.  Testing inversion algorithms against experimental data: 3D targets , 2009 .

[34]  A. Litman,et al.  Reconstruction by level sets of n-ary scattering obstacles , 2005 .

[35]  Ignace Bogaert,et al.  An efficient hybrid MLFMA-FFT solver for the volume integral equation in case of sparse 3D inhomogeneous dielectric scatterers , 2008, J. Comput. Phys..