Bayesian Compressive Sensing Approaches for the Reconstruction of Two-Dimensional Sparse Scatterers Under TE Illuminations

In this paper, the reconstruction of sparse scatterers under multiview transverse-electric illumination is dealt with. Starting from a probabilistic formulation of the “inverse source” problem, two Bayesian compressive sensing approaches are introduced. The former is a suitable extension of the single-task method presented earlier for the transverse-magnetic scalar case, while the other exploits an innovative multitask implementation to take into account the relationships among the “contrast currents” at the different probing views. Representative numerical results are discussed to assess, also comparatively, the numerical efficiency, the accuracy, and the robustness of the proposed approaches.

[1]  L. Blanc-Féraud,et al.  A new regularization scheme for inverse scattering , 1997 .

[2]  G. Franceschetti,et al.  On the degrees of freedom of scattered fields , 1989 .

[3]  L. E. Larsen,et al.  Limitations of Imaging with First-Order Diffraction Tomography , 1984 .

[4]  Motoyuki Sato,et al.  Foreword to the Special Issue on Subsurface Sensing Using Ground-Penetrating Radar (GPR) , 2007, IEEE Trans. Geosci. Remote. Sens..

[5]  Magda El-Shenawee,et al.  Level Set Algorithm for Shape Reconstruction of Non-Overlapping Three-Dimensional Penetrable Targets , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[6]  Tommaso Isernia,et al.  On the Solution of 2-D Inverse Scattering Problems via Source-Type Integral Equations , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[7]  J. Lovetri,et al.  A Novel Microwave Tomography System Using a Rotatable Conductive Enclosure , 2011, IEEE Transactions on Antennas and Propagation.

[8]  A. Massa,et al.  Iterative image reconstruction of two-dimensional scatterers illuminated by TE waves , 2006, IEEE Transactions on Microwave Theory and Techniques.

[9]  Andrea Massa,et al.  A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data , 2005 .

[10]  J. LoVetri,et al.  Comparison of an Enhanced Distorted Born Iterative Method and the Multiplicative-Regularized Contrast Source Inversion method , 2009, IEEE Transactions on Antennas and Propagation.

[11]  Takashi Takenaka,et al.  A Breast Imaging Model Using Microwaves and a Time Domain Three Dimensional Reconstruction Method , 2009 .

[12]  P. M. Berg,et al.  Contrast Source Inversion Method: State of Art , 2001 .

[13]  R.G. Baraniuk,et al.  Compressive Sensing [Lecture Notes] , 2007, IEEE Signal Processing Magazine.

[14]  Magda El-Shenawee,et al.  TE Versus TM for the Shape Reconstruction of 2-D PEC Targets Using the Level-Set Algorithm , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[15]  Ugur Cem Hasar.  Microwave nondestructive testing and evaluation of electrical properties of lossy materials , 2008 .

[16]  Manuel Benedetti,et al.  Multiple-Shape Reconstruction by Means of Multiregion Level Sets , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[17]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[18]  Dominique Lesselier,et al.  Special Section on Electromagnetic Imaging and Inversion of the Earth Sub-Surface , 2000 .

[19]  George Eastman House,et al.  Sparse Bayesian Learning and the Relevan e Ve tor Ma hine , 2001 .

[20]  Joyce R. McLaughlin,et al.  Recovery of the Lamé parameter μ in biological tissues , 2003 .

[21]  Paolo Rocca,et al.  A Bayesian-Compressive-Sampling-Based Inversion for Imaging Sparse Scatterers , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[22]  E.J. Candes.  Compressive Sampling , 2022 .

[23]  Michael E. Tipping,et al.  Analysis of Sparse Bayesian Learning , 2001, NIPS.

[24]  Dominique Lesselier,et al.  Foreword to the special section on electromagnetic and ultrasonic nondestructive evaluation , 2002 .

[25]  Q. Fang,et al.  Viable Three-Dimensional Medical Microwave Tomography: Theory and Numerical Experiments , 2010, IEEE Transactions on Antennas and Propagation.

[26]  Mario Bertero,et al.  Introduction to Inverse Problems in Imaging , 1998 .

[27]  Lawrence Carin,et al.  Bayesian Compressive Sensing , 2008, IEEE Transactions on Signal Processing.

[28]  A. Massa,et al.  Complex-Weight Sparse Linear Array Synthesis by Bayesian Compressive Sampling , 2012, IEEE Transactions on Antennas and Propagation.

[29]  David B. Dunson,et al.  Multitask Compressive Sensing , 2009, IEEE Transactions on Signal Processing.

[30]  Xudong Chen,et al.  An Improved Subspace-Based Optimization Method and Its Implementation in Solving Three-Dimensional Inverse Problems , 2010, IEEE Transactions on Geoscience and Remote Sensing.

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

[32]  Eric L. Miller,et al.  Spherical harmonics microwave algorithm for shape and location reconstruction of breast cancer tumor , 2006, IEEE Transactions on Medical Imaging.

[33]  Mahta Moghaddam,et al.  Inversion of Subsurface Properties of Layered Dielectric Structures With Random Slightly Rough Interfaces Using the Method of Simulated Annealing , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[34]  M. Pastorino.  Stochastic Optimization Methods Applied to Microwave Imaging: A Review , 2007, IEEE Transactions on Antennas and Propagation.

[35]  Matteo Pastorino,et al.  Numerical assessment concerning a focused microwave diagnostic method for medical applications , 2000 .

[36]  A. Massa,et al.  Bayesian Compressive Sampling for Pattern Synthesis With Maximally Sparse Non-Uniform Linear Arrays , 2011, IEEE Transactions on Antennas and Propagation.

[37]  Matteo Pastorino,et al.  Noninvasive imaging for the new century , 1999 .

[38]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[39]  Puyan Mojabi,et al.  On Super-Resolution With an Experimental Microwave Tomography System , 2010, IEEE Antennas and Wireless Propagation Letters.

[40]  A. Massa,et al.  A Nested Multi-Scaling Inexact-Newton Iterative Approach for Microwave Imaging , 2012, IEEE Transactions on Antennas and Propagation.

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

[42]  Matteo Pastorino,et al.  Short-Range Image-Based Method for the Inspection of Strong Scatterers Using Microwaves , 2006, IEEE Transactions on Instrumentation and Measurement.

[43]  Michael E. Tipping,et al.  Fast Marginal Likelihood Maximisation for Sparse Bayesian Models , 2003 .

[44]  A. Massa,et al.  Microwave medical imaging: potentialities and limitations of a stochastic optimization technique , 2004, IEEE Transactions on Microwave Theory and Techniques.

[45]  Takashi Takenaka,et al.  Conjugate gradient method applied to inverse scattering problem , 1995 .

[46]  P. Rocca,et al.  Differential Evolution as Applied to Electromagnetics , 2011, IEEE Antennas and Propagation Magazine.

[47]  Jean-Charles Bolomey,et al.  Quantitative Microwave Imaging for Breast Cancer Detection Using a Planar 2.45 GHz System , 2010, IEEE Transactions on Instrumentation and Measurement.

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

[49]  Eric L. Miller,et al.  Adaptive multiscale reconstruction of buried objects : Electromagnetic characterization of buried obstacles , 2004 .

[50]  Andrea Massa,et al.  Multiresolution subspace-based optimization method for inverse scattering problems. , 2011, Journal of the Optical Society of America. A, Optics, image science, and vision.

[51]  Tommaso Isernia,et al.  Electromagnetic inverse scattering: Retrievable information and measurement strategies , 1997 .

[52]  Puyan Mojabi,et al.  A Wideband Microwave Tomography System With a Novel Frequency Selection Procedure , 2010, IEEE Transactions on Biomedical Engineering.

[53]  A. Massa,et al.  Detection, location, and imaging of multiple scatterers by means of the iterative multiscaling method , 2004, IEEE Transactions on Microwave Theory and Techniques.

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

[55]  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.