A Qualitative Deep Learning Method for Inverse Scattering Problems
Keywords:
convolutional neural network, deep learning, inverse acoustic scattering, qualitative methodAbstract
In this paper, we propose a novel deep convolutional neural network (CNN) based qualitative learning method for solving the inverse scattering problem, which is notoriously difficult due to its highly nonlinearity and ill-posedness. The trained deep CNN accurately approximates the nonlinear mapping from the noisy far-field pattern (from measurements) to a disk that fits the location and size of the unknown scatterer. The used training data is derived from the simulated noisy-free far-field patterns of a large number of disks with different randomly generated centers and radii within the domain of interest. The reconstructed fitting disk is also very useful as a good initial guess for other established nonlinear optimization algorithms. Numerical results are presented to illustrate the promising reconstruction accuracy and efficiency of our proposed qualitative deep learning method.
Downloads
References
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer New York, 2012.
X. Liu and B. Zhang, “Recent progress on the factorization method for inverse acoustic scattering problems,” SCIENTIA SINICA Mathematica, vol. 45, pp. 873–890, 2015.
X. Liu, “A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency,” Inverse Problems, vol. 33, no. 8, p. 085011, 2017.
A. Roger, “Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem,” IEEE Transactions on Antennas and Propagation, vol. 29, no. 2, pp. 232–238, 1981.
G. Giorgi, M. Brignone, R. Aramini, and M. Piana, “Application of the Inhomogeneous Lippmann– Schwinger Equation to Inverse Scattering Problems,” SIAM Journal on Applied Mathematics, vol. 73, no. 1, pp. 212–231, 2013.
D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Problems, vol. 19, no. 6, pp. S105– S137, 2003.
R. Potthast, “A survey on sampling and probe methods for inverse problems,” Inverse Problems, vol. 22, no. 2, pp. R1–R47, 2006. [8] T. Arens and A. Lechleiter, “The linear sampling method revisited,” Journal of Integral Equations and Applications, vol. 21, no. 2, pp. 179–202, 2009.
F. Cakoni and D. Colton, A Qualitative Approach to Inverse Scattering Theory, Springer US, 2013.
A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, OUP Oxford, 2008.
K. H. Leem, J. Liu, and G. Pelekanos, “An adaptive quadrature-based factorization method for in verse acoustic scattering problems,” Inverse Problems in Science and Engineering, vol. 27, no. 3, pp. 299–316, 2019.
K. H. Leem, J. Liu, and G. Pelekanos, “Efficient Adaptive Qualitative Methods for 3D Inverse Scattering Problems,” ACES Journal, vol. 33, no. 10, 2018.
K. H. Leem, J. Liu, and G. Pelekanos, “Two direct factorization methods for inverse scattering problems,” Inverse Problems, vol. 34, no. 12, p. 125004, 2018.
M. Ikehata, E. Niemi, and S. Siltanen, “Inverse obstacle scattering with limited-aperture data,” Inverse Problems and Imaging, vol. 6, no. 1, pp. 77–94, 2012.
R. Potthast, J. Sylvester, and S. Kusiak, “A range test for determining scatterers with unknown physical properties,” Inverse Problems, vol. 19, no. 3, pp. 533–547, 2003.
J. Liu and J. Sun, “Extended sampling method in inverse scattering,” Inverse Problems, vol. 34, no. 8, p. 085007, 2018.
K. H. Leem, J. Liu, and G. Pelekanos, “An extended direct factorization method for inverse scattering with limited aperture data,” Inverse Problems in Science and Engineering, p. to appear, 2019.
F. Rosenblatt, Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms, Spartan Books, Washington DC, 1961.
M. A. Kramer, “Nonlinear principal component analysis using autoassociative neural networks,” AIChE Journal, vol. 37, no. 2, pp. 233–243, 1991.
K. Fukushima, “Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position,” Biological Cybernetics, vol. 36, no. 4, pp. 193–202, 1980.
O. Ronneberger, P. Fischer, and T. Brox, “U-Net: Convolutional Networks for Biomedical Image Segmentation,” arXiv preprint, vol. arXiv:1505.04597, 2015.
S. Hochreiter and J. Schmidhuber, “Long shortterm memory,” Neural Computation, vol. 9, no. 8, pp. 1735–1780, 1997.
A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” Communications of the ACM, vol. 60, no. 6, pp. 84–90, 2017.
H. Kabir, Y. Cao, Y. Cao, and Q. Zhang, “Advances of neural network modeling methods for RF/microwave applications,” ACES Journal, vol. 25, no. 5, p. 423, 2010.
Z. Wei and X. Chen, “Deep-learning schemes for full-wave nonlinear inverse scattering problems,” IEEE Transactions on Geoscience and Remote Sensing, vol. 57, no. 4, pp. 1849–1860, 2019.
H. Yao, M. Li, and L. Jiang, “Applying deep learning approach to the far-field subwavelength imaging based on near-field resonant metalens at microwave frequencies,” IEEE Access, vol. 7, pp. 63801–63808, 2019.
Y. Khoo and L. Ying, “SwitchNet: a neural network model for forward and inverse scattering problems,” SIAM Journal on Scientific Computing, vol. 41, no. 5, pp. 3182–3201, 2019.
R. D. Murch, D. G. H. Tan, and D. J. N. Wall, “Newton-Kantorovich method applied to two-dimensional inverse scattering for an exterior Helmholtz problem,” Inverse Problems, vol. 4, no. 4, pp. 1117–1128, 1988.
J. Adler and O. Öktem, “Solving ill-posed inverse problems using iterative deep neural networks,” Inverse Problems, vol. 33, no. 12, p. 124007, 2017.
L. Li, L. G. Wang, F. L. Teixeira, C. Liu, A. Nehorai, and T. J. Cui, “DeepNIS: Deep neural network for nonlinear electromagnetic inverse scattering,” IEEE Transactions on Antennas and Propagation, vol. 67, no. 3, pp. 1819–1825, 2018.
Y. Sanghvi, Y. N. G. B. Kalepu, and U. Khankhoje, “Embedding Deep Learning in Inverse Scattering Problems,” IEEE Transactions on Computational Imaging, 2019.
L. Li, L. G. Wang, D. O. Acero, and F. L. Teixeira, “Deep Convolutional Neural Network Approach for Solving Nonlinear Inverse Scattering Problems,” in 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, pp. 219–220, IEEE, 2019.
Z. Wei and X. Chen, “Physics-Inspired Convolutional Neural Network for Solving Full-Wave Inverse Scattering Problems,” IEEE Transactions on Antennas and Propagation, vol. 67, no. 9, pp. 6138– 6148, 2019.
H. Yang, H. Yu, and G. Wang, “Deep learning for the classification of lung nodules,” arXiv preprint, vol. axXiv:1611.06651v2, 2017.
H. Yang, W.-X. Cong, and G. Wang, “Deep learning for dual-energy X-ray computed tomography,” Proceedings of The 14th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, pp. 864–869, 2017.
N. Srivastava, G. E. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, “Dropout: a simple way to prevent neural networks from overfitting,” Journal of Machine Learning Research, vol. 15, pp. 1929–1958, 2014.
