A Multithreshold Iterative DBIM-Based Algorithm for the Imaging of Heterogeneous Breast Tissues

Objective: This paper proposes a novel microwave imaging (MWI) multifrequency technique, which combines compressive sensing (CS) with the well-known distorted Born iterative method. CS strategies are emerging as a promising tool in MWI applications, which can improve reconstruction quality and/or reduce the number of data samples. Methods: The proposed approach is based on iterative shrinkage thresholding algorithm (ISTA), which has been modified to include an automatic and adaptive selection of multithreshold values. Results: This adaptive multithreshold ISTA implementation is applied in reconstruction of two-dimensional (2-D) numerical heterogeneous breast phantoms, where it outperforms the standard thresholding implementation. We show that our approach is also successful in 3-D simulations of a realistic imaging experiment, despite the mismatch between the data and our algorithm's forward model. Conclusion: These results suggest that the proposed algorithm is a promising tool for medical MWI applications. Significance: Important novelties of this approach are the use of multiple thresholds to recover the different unknowns in the Debye model as well as the adaptive selection of these thresholds. Moreover, we have shown that employing modified hard constraints inside the linear step of the inversion procedure can enhance reconstruction quality.

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

[2]  John A. Hudson,et al.  The use of the Born approximation in seismic scattering problems , 1981 .

[3]  Joe LoVetri,et al.  Monitoring breast cancer treatment progress with microwave tomography and radar-based tissue-regions estimation , 2015, 2015 9th European Conference on Antennas and Propagation (EuCAP).

[4]  Panagiotis Kosmas,et al.  Multiple-Frequency DBIM-TwIST Algorithm for Microwave Breast Imaging , 2017, IEEE Transactions on Antennas and Propagation.

[5]  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.

[6]  Paul M. Meaney,et al.  Microwave tomographic imaging for breast cancer chemotherapy monitoring , 2014, The 8th European Conference on Antennas and Propagation (EuCAP 2014).

[7]  Lorenzo Crocco,et al.  On quantitative microwave tomography of female breast , 2009 .

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

[9]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[10]  Holger Rauhut,et al.  A Mathematical Introduction to Compressive Sensing , 2013, Applied and Numerical Harmonic Analysis.

[11]  M. Pastorino,et al.  A Novel Microwave Imaging Approach Based on Regularization in $L^{p}$ Banach Spaces , 2012, IEEE Transactions on Antennas and Propagation.

[12]  Panagiotis Kosmas,et al.  Towards a microwave imaging prototype based on the DBIM-TwIST algorithm and a custom-made transceiver system , 2017, 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA).

[13]  Susan C. Hagness,et al.  High-Resolution Microwave Breast Imaging Using a 3-D Inverse Scattering Algorithm With a Variable-Strength Spatial Prior Constraint , 2017 .

[14]  Bertolt Eicke.  Iteration methods for convexly constrained ill-posed problems in hilbert space , 1992 .

[15]  Vito Pascazio,et al.  A nonlinear estimation method in tomographic imaging , 1997, IEEE Trans. Geosci. Remote. Sens..

[16]  Panagiotis Kosmas,et al.  Three-Dimensional Microwave Breast Imaging: Dispersive Dielectric Properties Estimation Using Patient-Specific Basis Functions , 2009, IEEE Transactions on Medical Imaging.

[17]  M. Lindstrom,et al.  A large-scale study of the ultrawideband microwave dielectric properties of normal breast tissue obtained from reduction surgeries , 2007, Physics in medicine and biology.

[18]  Panagiotis Kosmas,et al.  Microwave breast imaging based on an optimized two-step iterative shrinkage/thresholding method , 2015, 2015 9th European Conference on Antennas and Propagation (EuCAP).

[19]  Lorenzo Crocco,et al.  On the Optimal Measurement Configuration for Magnetic Nanoparticles-Enhanced Breast Cancer Microwave Imaging , 2015, IEEE Transactions on Biomedical Engineering.

[20]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[21]  P. Kosmas,et al.  A matched-filter FDTD-based time reversal approach for microwave breast cancer detection , 2006, IEEE Transactions on Antennas and Propagation.

[22]  S. Noghanian,et al.  Analysis of Incident Field Modeling and Incident/Scattered Field Calibration Techniques in Microwave Tomography , 2011, IEEE Antennas and Wireless Propagation Letters.

[23]  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.

[24]  Panagiotis Kosmas,et al.  Microwave Medical Imaging Based on Sparsity and an Iterative Method With Adaptive Thresholding , 2015, IEEE Transactions on Medical Imaging.

[25]  Lorenzo Crocco,et al.  A Simple Quantitative Inversion Approach for Microwave Imaging in Embedded Systems , 2015 .

[26]  Vito Pascazio,et al.  An adaptive multi-threshold iterative shrinkage algorithm for microwave imaging applications , 2016, 2016 10th European Conference on Antennas and Propagation (EuCAP).

[27]  Antonin Chambolle,et al.  Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage , 1998, IEEE Trans. Image Process..

[28]  Wolfgang Osten,et al.  Introduction to Inverse Problems in Imaging , 1999 .

[29]  K. Paulsen,et al.  Initial clinical experience with microwave breast imaging in women with normal mammography. , 2007, Academic radiology.

[30]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

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

[32]  Zongben Xu,et al.  Fast Compressed Sensing SAR Imaging Based on Approximated Observation , 2013, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[33]  Aswin C. Sankaranarayanan,et al.  Compressive Sensing , 2008, Computer Vision, A Reference Guide.

[34]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

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

[36]  Joel A. Tropp,et al.  Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit , 2006, Signal Process..

[37]  Paul M. Meaney,et al.  Fast 3-D Tomographic Microwave Imaging for Breast Cancer Detection , 2012, IEEE Transactions on Medical Imaging.

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

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

[40]  Puyan Mojabi,et al.  Enhancement of Gauss–Newton Inversion Method for Biological Tissue Imaging , 2013, IEEE Transactions on Microwave Theory and Techniques.

[41]  A. Preece,et al.  Microwave Radar-Based Breast Cancer Detection: Imaging in Inhomogeneous Breast Phantoms , 2009, IEEE Antennas and Wireless Propagation Letters.

[42]  Niederauer Mastelari,et al.  Guidelines for effective microwave breast imaging: A numerical assessment against 3D anthropomorphic phantoms , 2010, Proceedings of the Fourth European Conference on Antennas and Propagation.

[43]  Joe LoVetri,et al.  A 3-D Dual-Polarized Near-Field Microwave Imaging System , 2014, IEEE Transactions on Microwave Theory and Techniques.

[44]  Lorenzo Crocco,et al.  Exploiting compressive sensing in microwave tomography and inverse scattering , 2014, The 8th European Conference on Antennas and Propagation (EuCAP 2014).

[45]  Olgica Milenkovic,et al.  Subspace Pursuit for Compressive Sensing Signal Reconstruction , 2008, IEEE Transactions on Information Theory.

[46]  Lorenzo Crocco,et al.  Wavelet-Based Regularization for Robust Microwave Imaging in Medical Applications , 2015, IEEE Transactions on Biomedical Engineering.

[47]  Massimo Fornasier,et al.  Compressive Sensing , 2015, Handbook of Mathematical Methods in Imaging.

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

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

[50]  Giovanni Leone,et al.  Inverse scattering under the distorted Born approximation for cylindrical geometries , 1999 .

[51]  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.

[52]  Eytan Domany,et al.  The Born approximation in the theory of the scattering of elastic waves by flaws , 1977 .

[53]  José M. Bioucas-Dias,et al.  A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration , 2007, IEEE Transactions on Image Processing.

[54]  G. Franceschetti,et al.  On the spatial bandwidth of scattered fields , 1987 .

[55]  J. Lovetri,et al.  Enhancement of the Krylov Subspace Regularization for Microwave Biomedical Imaging , 2009, IEEE Transactions on Medical Imaging.

[56]  Aleksandra Pizurica,et al.  Quantitative microwave imaging based on a huber regularization , 2013 .

[57]  Vito Pascazio,et al.  Statistical regularization in linearized microwave imaging through MRF-based MAP estimation: hyperparameter estimation and image computation , 2003, IEEE Trans. Image Process..

[58]  Vito Pascazio,et al.  Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies , 2000, IEEE Trans. Geosci. Remote. Sens..

[59]  Lorenzo Crocco,et al.  A FEASIBILITY STUDY ON MICROWAVE IMAGING FOR BRAIN STROKE MONITORING , 2012 .

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

[61]  Lei Liang,et al.  Adaptive Landweber method to deblur images , 2003, IEEE Signal Process. Lett..

[62]  Siyuan Chen,et al.  Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using the distorted Born iterative method , 2001, IEEE Trans. Geosci. Remote. Sens..

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

[64]  Rosa Scapaticci,et al.  Magnetic nanoparticles enhanced breast cancer microwave imaging via compressive sensing , 2015, 2015 9th European Conference on Antennas and Propagation (EuCAP).

[65]  Stephen D. Gedney,et al.  Convolution PML (CPML): An efficient FDTD implementation of the CFS–PML for arbitrary media , 2000 .

[66]  Mario R. Casu,et al.  A COTS-Based Microwave Imaging System for Breast-Cancer Detection , 2017, IEEE Transactions on Biomedical Circuits and Systems.

[67]  Paolo Rocca,et al.  Compressive Sensing in Electromagnetics - A Review , 2015, IEEE Antennas and Propagation Magazine.