MT – BCS-Based Microwave Imaging Approach Through Minimum-Norm Current Expansion

An innovative three-step technique based on the multi-task Bayesian compressive sensing (MT - BCS) strategy is introduced to image 2D-sparse dielectric profiles. The proposed approach reformulates the contrast source mathematical description of the inversion problem into two fictitious real-valued ones jointly solved through a fast Relevance Vector Machine by taking into account the inter-relationships between the real and the imaginary parts of the unknown equivalent currents. Selected results from a numerical validation are presented and discussed to comparatively assess the accuracy, the robustness, and the computational efficiency of the proposed implementation.

[1]  H. Lev-Ari,et al.  Compressive Sensing for Inverse Scattering , 2008 .

[2]  Edwin A. Marengo COMPRESSIVE SENSING AND SIGNAL SUBSPACE METHODS FOR INVERSE SCATTERING INCLUDING MULTIPLE SCATTERING , 2007 .

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

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

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

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

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

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

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

[10]  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.

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

[12]  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.

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

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

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

[16]  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.

[17]  P. Rocca,et al.  Iterative multi-resolution retrieval of non-measurable equivalent currents for the imaging of dielectric objects , 2009 .

[18]  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.

[19]  A. Massa,et al.  Microwave Imaging Within the First-Order Born Approximation by Means of the Contrast-Field Bayesian Compressive Sensing , 2012, IEEE Transactions on Antennas and Propagation.

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

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

[22]  A. Fannjiang,et al.  Compressive inverse scattering: I. High-frequency SIMO/MISO and MIMO measurements , 2009, 0906.5405.

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

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

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

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

[27]  A. Fannjiang,et al.  Compressive inverse scattering: II. Multi-shot SISO measurements with born scatterers , 2010 .

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

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

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

[31]  E. A. Marengo Subspace and Bayesian Compressive Sensing Methods in Imaging , 2007 .

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

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

[34]  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.

[35]  A Massa,et al.  Bayesian compressive optical imaging within the Rytov approximation. , 2012, Optics letters.

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

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

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

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

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

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

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

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

[44]  Eric L. Miller,et al.  Adaptive multiscale reconstruction of buried objects , 2004 .

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