A Linear Model for Microwave Imaging of Highly Conductive Scatterers

In this paper, a linear model based on multiple measurement vectors’ model is proposed to formulate the inverse scattering problem of highly conductive objects at one single frequency. Considering the induced currents that are mostly distributed on the boundaries of the scatterers, joint sparse structure is enforced by a sum-of-norm regularization. Since no a priori information is required and no approximation of the scattering model has been made, the proposed method is versatile. Imaging results with transverse magnetic and transverse electric polarized synthetic data and Fresnel data demonstrate its higher resolving ability than both linear sampling method and its improved version with higher, but acceptable, computational complexity.

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

[2]  T. Isernia,et al.  An Improved Simple Method for Imaging the Shape of Complex Targets , 2013, IEEE Transactions on Antennas and Propagation.

[3]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[4]  P. Rocca,et al.  Evolutionary optimization as applied to inverse scattering problems , 2009 .

[5]  J. M. Martínez,et al.  Inexact spectral projected gradient methods on convex sets , 2003 .

[6]  Yahya Rahmat-Samii,et al.  The field equivalence principle: illustration of the establishment of the non-intuitive null fields , 2000 .

[7]  José Mario Martínez,et al.  Nonmonotone Spectral Projected Gradient Methods on Convex Sets , 1999, SIAM J. Optim..

[8]  A. Yarovoy,et al.  Solving the PEC inverse scattering problem with a linear model , 2016, 2016 URSI International Symposium on Electromagnetic Theory (EMTS).

[9]  T. Isernia,et al.  The Linear Sampling Method as a Way to Quantitative Inverse Scattering , 2012, IEEE Transactions on Antennas and Propagation.

[10]  A. Roger,et al.  Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem , 1981 .

[11]  Anyong Qing,et al.  Electromagnetic inverse scattering of multiple two-dimensional perfectly conducting objects by the differential evolution strategy , 2003 .

[12]  T. Isernia,et al.  On Simple Methods for Shape Reconstruction of Unknown Scatterers , 2007, IEEE Transactions on Antennas and Propagation.

[13]  Michael P. Friedlander,et al.  Probing the Pareto Frontier for Basis Pursuit Solutions , 2008, SIAM J. Sci. Comput..

[14]  丸山 徹.  Convex Analysisの二,三の進展について , 1977 .

[15]  Salvatore Caorsi,et al.  Inverse‐scattering method for dielectric objects based on the reconstruction of the nonmeasurable equivalent current density , 1999 .

[16]  A. Kirsch,et al.  A simple method for solving inverse scattering problems in the resonance region , 1996 .

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

[18]  Roger Fletcher,et al.  Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming , 2005, Numerische Mathematik.

[19]  J. Nagy,et al.  Numerical Linear Algebra for Nonlinear Microwave Imaging Numerical Linear Algebra for Nonlinear Microwave Imaging * , 2008 .

[20]  P. M. van den Berg,et al.  Two‐dimensional location and shape reconstruction , 1994 .

[21]  Michael P. Friedlander,et al.  Theoretical and Empirical Results for Recovery From Multiple Measurements , 2009, IEEE Transactions on Information Theory.

[22]  T. Arens,et al.  Why linear sampling works , 2004 .

[23]  Matteo Pastorino,et al.  A crack identification microwave procedure based on a genetic algorithm for nondestructive testing , 2001 .

[24]  Rachel Ward,et al.  Compressed Sensing With Cross Validation , 2008, IEEE Transactions on Information Theory.

[25]  M. Dehmollaian,et al.  Three-Dimensional Near-Field Microwave Imaging Using Hybrid Linear Sampling and Level Set Methods in a Medium With Compact Support , 2014, IEEE Transactions on Antennas and Propagation.

[26]  Michael P. Friedlander,et al.  Sparse Optimization with Least-Squares Constraints , 2011, SIAM J. Optim..

[27]  D. Colton,et al.  A simple method using Morozov's discrepancy principle for solving inverse scattering problems , 1997 .

[28]  A.J. Devaney.  Time reversal imaging of obscured targets from multistatic data , 2005, IEEE Transactions on Antennas and Propagation.

[29]  M. Saillard,et al.  Special section: Testing inversion algorithms against experimental data , 2001 .

[30]  Qing Huo Liu,et al.  Inversion of multi-frequency experimental data for imaging complex objects by a DTA–CSI method , 2005 .

[31]  Ali Mohammad-Djafari,et al.  Microwave imaging of inhomogeneous objects made of a finite number of dielectric and conductive materials from experimental data , 2005 .

[32]  J. Hadamard,et al.  Lectures on Cauchy's Problem in Linear Partial Differential Equations , 1924 .

[33]  A. Massa,et al.  Multifrequency Particle Swarm Optimization for Enhanced Multiresolution GPR Microwave Imaging , 2017, IEEE Transactions on Geoscience and Remote Sensing.

[34]  Federico Viani,et al.  MT – BCS-Based Microwave Imaging Approach Through Minimum-Norm Current Expansion , 2013, IEEE Transactions on Antennas and Propagation.

[35]  Jong Chul Ye,et al.  Compressive Diffuse Optical Tomography: Noniterative Exact Reconstruction Using Joint Sparsity , 2011, IEEE Transactions on Medical Imaging.

[36]  Anyong Qing.  Electromagnetic inverse scattering of multiple perfectly conducting cylinders by differential evolution strategy with individuals in groups (GDES) , 2004, IEEE Transactions on Antennas and Propagation.

[37]  Tian Jin,et al.  Cross-Correlated Contrast Source Inversion , 2017, IEEE Transactions on Antennas and Propagation.

[38]  Tian Jin,et al.  Novel Methods to Accelerate CS Radar Imaging by NUFFT , 2015, IEEE Transactions on Geoscience and Remote Sensing.

[39]  Bojan B. Guzina,et al.  A linear sampling method for near-field inverse problems in elastodynamics , 2004 .

[40]  Yuantao Gu,et al.  Cross Validation in Compressive Sensing and its Application of OMP-CV Algorithm , 2016, ArXiv.

[41]  Ewout van den Berg,et al.  Convex optimization for generalized sparse recovery , 2009 .