Two-Step Enhanced Deep Learning Approach for Electromagnetic Inverse Scattering Problems

In this letter, a new deep learning (DL) approach is proposed to solve the electromagnetic inverse scattering (EMIS) problems. The conventional methods for solving inverse problems face various challenges including strong ill-conditions, high contrast, expensive computation cost, and unavoidable intrinsic nonlinearity. To overcome these issues, we propose a new two-step machine learning based approach. In the first step, a complex-valued deep convolutional neural network is employed to retrieve initial contrasts (permittivities) of dielectric scatterers from measured scattering data. In the second step, the previously obtained contrasts are input into a complex-valued deep residual convolutional neural network to refine the reconstruction of images. Consequently, the EMIS problem can be solved with much higher accuracy even for high-contrast objects. Numerical examples have demonstrated the capability of the newly proposed method with the improved accuracy. The proposed DL approach for EMIS problem serves a new path for realizing real-time quantitative microwave imaging for high-contrast objects.

[1]  Paolo Gamba,et al.  Electromagnetic detection of dielectric cylinders by a neural network approach , 1999, IEEE Trans. Geosci. Remote. Sens..

[2]  Xudong Chen,et al.  Computational Methods for Electromagnetic Inverse Scattering , 2018 .

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

[4]  Xudong Chen,et al.  Deep-Learning Schemes for Full-Wave Nonlinear Inverse Scattering Problems , 2019, IEEE Transactions on Geoscience and Remote Sensing.

[5]  Ji Wu,et al.  Study on a Poisson's equation solver based on deep learning technique , 2017, 2017 IEEE Electrical Design of Advanced Packaging and Systems Symposium (EDAPS).

[6]  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 .

[7]  Michael Unser,et al.  Deep Convolutional Neural Network for Inverse Problems in Imaging , 2016, IEEE Transactions on Image Processing.

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

[9]  Haipeng Wang,et al.  Target Classification Using the Deep Convolutional Networks for SAR Images , 2016, IEEE Transactions on Geoscience and Remote Sensing.

[10]  Minh N. Do,et al.  The Nonsubsampled Contourlet Transform: Theory, Design, and Applications , 2006, IEEE Transactions on Image Processing.

[11]  Xudong Chen,et al.  Subspace-Based Optimization Method for Solving Inverse-Scattering Problems , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[12]  Hugues Giovannini,et al.  Experimental demonstration of quantitative imaging beyond Abbe's limit with optical diffraction tomography. , 2009, Physical review letters.

[13]  Huanxin Zou,et al.  Deep Convolutional Highway Unit Network for SAR Target Classification With Limited Labeled Training Data , 2017, IEEE Geoscience and Remote Sensing Letters.

[14]  Yuanyuan Zhang,et al.  Adaptive Convolutional Neural Network and Its Application in Face Recognition , 2016, Neural Processing Letters.

[15]  He Ming Yao,et al.  Transient Heterogeneous Electromagnetic Simulation With DGTD and Behavioral Macromodel , 2017, IEEE Transactions on Electromagnetic Compatibility.

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

[17]  P. Chaumet,et al.  Superresolution in total internal reflection tomography. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[18]  Phil Kim,et al.  MATLAB Deep Learning , 2017, Apress.

[19]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[20]  He Ming Yao,et al.  Applying Convolutional Neural Networks for the Source Reconstruction , 2018 .

[21]  Lorenzo Crocco,et al.  Testing the contrast source extended Born inversion method against real data: the TM case , 2005 .

[22]  Paolo Rocca,et al.  Learning-by-examples techniques as applied to electromagnetics , 2018 .

[23]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[24]  He Ming Yao,et al.  Machine learning based method of moments (ML-MoM) , 2017, 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting.

[25]  M. Cátedra.  The CG-FFT Method: Application of Signal Processing Techniques to Electromagnetics , 1995 .

[26]  Lianlin Li,et al.  Complex-Valued Deep Convolutional Networks for Nonlinear Electromagnetic Inverse Scattering , 2018, 2018 IEEE International Conference on Computational Electromagnetics (ICCEM).

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

[28]  Jin Keun Seo,et al.  A Learning-Based Method for Solving Ill-Posed Nonlinear Inverse Problems: A Simulation Study of Lung EIT , 2018, SIAM J. Imaging Sci..

[29]  S. J. Hamilton,et al.  Deep D-Bar: Real-Time Electrical Impedance Tomography Imaging With Deep Neural Networks , 2017, IEEE Transactions on Medical Imaging.

[30]  Li Fei-Fei,et al.  Perceptual Losses for Real-Time Style Transfer and Super-Resolution , 2016, ECCV.

[31]  Michael A. Fiddy,et al.  Introduction to Imaging from Scattered Fields , 2014 .

[32]  Lianlin Li,et al.  DeepNIS: Deep Neural Network for Nonlinear Electromagnetic Inverse Scattering , 2018, IEEE Transactions on Antennas and Propagation.

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

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

[35]  W. Chew,et al.  Study of some practical issues in inversion with the Born iterative method using time-domain data , 1993 .

[36]  Howard Besser,et al.  Introduction to Imaging , 2003 .

[37]  Xiaoou Tang,et al.  Image Super-Resolution Using Deep Convolutional Networks , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[38]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[39]  Sergey Ioffe,et al.  Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift , 2015, ICML.

[40]  Jian Sun,et al.  Deep Residual Learning for Image Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[41]  Y. Rahmat-Samii,et al.  Particle swarm optimization in electromagnetics , 2004, IEEE Transactions on Antennas and Propagation.

[42]  Ulugbek Kamilov,et al.  Efficient and accurate inversion of multiple scattering with deep learning , 2018, Optics express.

[43]  Fernando L. Teixeira,et al.  Performance Analysis and Dynamic Evolution of Deep Convolutional Neural Network for Electromagnetic Inverse Scattering , 2019, IEEE Antennas and Wireless Propagation Letters.

[44]  Xudong Chen,et al.  Improving the Performances of the Contrast Source Extended Born Inversion Method by Subspace Techniques , 2013, IEEE Geoscience and Remote Sensing Letters.

[45]  He Ming Yao,et al.  Embedding the Behavior Macromodel Into TDIE for Transient Field-Circuit Simulations , 2016, IEEE Transactions on Antennas and Propagation.

[46]  Ioannis T. Rekanos,et al.  Inverse scattering of dielectric cylinders by using radial basis function neural networks , 2001 .

[47]  Thomas Brox,et al.  U-Net: Convolutional Networks for Biomedical Image Segmentation , 2015, MICCAI.