An Improved Deep Learning Scheme for Solving 2-D and 3-D Inverse Scattering Problems

Reconstructing the exact electromagnetic property of unknown targets from the measured scattered field is challenging due to the intrinsic nonlinearity and ill-posedness. In this paper, a new scheme, named the modified contrast scheme (MCS), is proposed to tackle nonlinear inverse scattering problems (ISPs). A local-wave amplifier coefficient is used to form the modified contrast, which is able to alleviate the global nonlinearity in original ISPs without decreasing the accuracy of the problem formulation. Moreover, the modified contrast is more suitable to be the input of the deep learning scheme, due to the unity bound of the modified contrast. Numerical results show that MCS with the modified contrast input performs well in both twodimensional (2D) and three-dimensional (3D) testing examples in real time after offline training process, even in high relative permittivity cases. Compared with the dominant current scheme, a significant improvement is achieved in reconstructing high contrast scatterers.

[1]  Rui Guo,et al.  Supervised Descent Learning Technique for 2-D Microwave Imaging , 2019, IEEE Transactions on Antennas and Propagation.

[2]  Xudong Chen,et al.  Subspace-Based Distorted-Born Iterative Method for Solving Inverse Scattering Problems , 2017, IEEE Transactions on Antennas and Propagation.

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

[4]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.

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

[6]  John Stang,et al.  Learning-Assisted Multimodality Dielectric Imaging , 2020, IEEE Transactions on Antennas and Propagation.

[7]  Xudong Chen,et al.  Non-Iterative Methods Based on Singular Value Decomposition for Inverse Scattering Problems , 2020, IEEE Transactions on Antennas and Propagation.

[8]  Reza Zoughi,et al.  Microwave non-destructive testing and evaluation , 2000 .

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

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

[11]  Feng Xu,et al.  Iterative Nonlinear Tikhonov Algorithm With Constraints for Electromagnetic Tomography , 2012, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[12]  Feng Han,et al.  Fast Electromagnetic Inversion of Inhomogeneous Scatterers Embedded in Layered Media by Born Approximation and 3-D U-Net , 2020, IEEE Geoscience and Remote Sensing Letters.

[13]  Yash Sanghvi,et al.  Embedding Deep Learning in Inverse Scattering Problems , 2020, IEEE Transactions on Computational Imaging.

[14]  P. M. Berg,et al.  Imaging of biomedical data using a multiplicative regularized contrast source inversion method , 2002 .

[15]  Li Jun Jiang,et al.  Two-Step Enhanced Deep Learning Approach for Electromagnetic Inverse Scattering Problems , 2019, IEEE Antennas and Wireless Propagation Letters.

[16]  M. Moghaddam,et al.  Inverse Scattering Using a Joint $L1-L2$ Norm-Based Regularization , 2016, IEEE Transactions on Antennas and Propagation.

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

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

[19]  Lorenzo Crocco,et al.  An Algebraic Solution Method for Nonlinear Inverse Scattering , 2015, IEEE Transactions on Antennas and Propagation.

[20]  Yu Zhong,et al.  Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems , 2019, J. Imaging.

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

[22]  Andrea Massa,et al.  Compressive Sensing Imaging of Non-Sparse 2D Scatterers by a Total-Variation Approach Within the Born Approximation , 2014, IEEE Transactions on Antennas and Propagation.

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

[24]  Yu Tsao,et al.  End-to-End Waveform Utterance Enhancement for Direct Evaluation Metrics Optimization by Fully Convolutional Neural Networks , 2017, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

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

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

[27]  Dominique Lesselier,et al.  Fast Full-Wave Analysis of Damaged Periodic Fiber-Reinforced Laminates , 2018, IEEE Transactions on Antennas and Propagation.

[28]  M. Salucci,et al.  DNNs as Applied to Electromagnetics, Antennas, and Propagation—A Review , 2019, IEEE Antennas and Wireless Propagation Letters.

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

[30]  Xudong Chen,et al.  Physics-Inspired Convolutional Neural Network for Solving Full-Wave Inverse Scattering Problems , 2019, IEEE Transactions on Antennas and Propagation.

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

[32]  Thomas Brox,et al.  3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation , 2016, MICCAI.

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

[34]  D. Lesselier,et al.  A New Integral Equation Method to Solve Highly Nonlinear Inverse Scattering Problems , 2016, IEEE Transactions on Antennas and Propagation.

[35]  P. M. Berg,et al.  Extended contrast source inversion , 1999 .

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

[37]  A. Devaney.  Inverse-scattering theory within the Rytov approximation. , 1981, Optics letters.