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DeepNIS: Deep Neural Network for Nonlinear Electromagnetic Inverse Scattering
Lianlin Li, Long Gang Wang, Fernando L. Teixeira, Che Liu, Arye Nehora, Tie Jun Cui
TL;DR
Nonlinear EM inverse scattering supports accurate, nondestructive imaging but conventional approaches struggle with computational demands, especially for large scenes and high-contrast objects. DeepNIS connects DNN architecture with iterative inverse-scattering methods through cascaded complex-valued residual CNN modules, and demonstrations report better image quality and computational time than conventional techniques.
Problem
Nonlinear EM inverse scattering is an accurate, nondestructive imaging tool, but conventional methods are impractical for large scenes and high-contrast objects.
Method
DeepNIS connects CNN architecture with unfolded iterative nonlinear EM inverse-scattering solutions using cascaded multi-layer complex-valued residual CNN modules as a non-iterative solver.
Results
Numerical and experimental demonstrations show that DeepNIS outperforms conventional nonlinear inverse-scattering techniques in image quality and computational time.
Takeaways & Limitations
DeepNIS is suitable for large-scale nonlinear EM inverse scattering because its non-iterative, parallelizable convolution operations reduce computational costs.
Takeaways & Limitations
Adding convolutional layers can enrich system nonlinearity but increases model complexity, training time, and overfitting risk.
Abstract
from arXiv · showhide
Nonlinear electromagnetic (EM) inverse scattering is a quantitative and super-resolution imaging technique, in which more realistic interactions between the internal structure of scene and EM wavefield are taken into account in the imaging procedure, in contrast to conventional tomography. However, it poses important challenges arising from its intrinsic strong nonlinearity, ill-posedness, and expensive computation costs. To tackle these difficulties, we, for the first time to our best knowledge, exploit a connection between the deep neural network (DNN) architecture and the iterative method of nonlinear EM inverse scattering. This enables the development of a novel DNN-based methodology for nonlinear EM inverse problems (termed here DeepNIS). The proposed DeepNIS consists of a cascade of multi-layer complexvalued residual convolutional neural network (CNN) modules. We numerically and experimentally demonstrate that the DeepNIS outperforms remarkably conventional nonlinear inverse scattering methods in terms of both the image quality and computational time. We show that DeepNIS can learn a general model approximating the underlying EM inverse scattering system. It is expected that the DeepNIS will serve as powerful tool in treating highly nonlinear EM inverse scattering problems over different frequency bands, involving large-scale and high-contrast objects, which are extremely hard and impractical to solve using conventional inverse scattering methods.
I. INTRODUCTION
Nonlinear EM inverse scattering provides quantitative imaging that accounts for multiple scattering but remains strongly nonlinear, ill-posed, and computationally expensive. DeepNIS addresses these challenges by connecting DNN architectures with iterative inverse-scattering methods and demonstrates improved image quality and computational speed.
- Nonlinear EM inverse scattering accounts for multiple scattering and can reveal scene structure quantitatively beyond conventional tomography.
- The field has developed deterministic optimization and stochastic inverse-scattering algorithms, while deep learning has become powerful for regression, classification, and image-processing tasks.
- DeepNIS establishes a connection between DNN architectures and iterative nonlinear EM inverse-scattering methods.
- DeepNIS uses cascaded complex-valued residual CNN modules that approximately characterize multiple scattering and process a BP image through successive refinements.
- Numerical MNIST and Fresnel experimental demonstrations report that DeepNIS outperforms conventional nonlinear inverse-scattering techniques in image quality and computational time.
II. PROBLEM STATEMENT
The paper motivates DNNs as an efficient alternative for nonlinear EM inverse scattering because iterative solutions require convolution operations while accounting for nonlinearities.
- DNNs may provide an efficient alternative to iterative nonlinear EM inverse-scattering solutions because those solutions require convolutions and nonlinear processing.
II.A. Connection between DNN and nonlinear EM inverse scattering
The nonlinear EM inverse-scattering problem models scattered and total fields through coupled equations over a discretized investigation domain. Its iterative, regularized updates can be reorganized into a DNN-like recursion whose learned parameters motivate DeepNIS.
- Measurement configuration: A 2D MIMO configuration illuminates the investigation domain with multiple TM-polarized waves while receivers outside the domain collect scattered fields.
- Coupled inverse problem: The contrast function is defined from the squared sample and background wavenumbers as χ = k^2/k_0^2 − 1.
- Coupled inverse problem: The discretized inverse problem solves coupled equations relating scattered fields, total fields, contrast currents, and contrast functions.
- Iterative solution: Iterative contrast-function updates use a Jacobian-based data term and regularization to address the inherent ill-posedness of electromagnetic inverse scattering.
- Iterative solution: A sparse-transform regularizer and proximal approximation produce a soft-thresholding update for the contrast function.
- DNN connection: Rearranging the recursive solution reveals a DNN analogy in which the iteration index is a layer, learned matrices and biases are parameters, and soft thresholding is activation.
- DNN connection: Training layer parameters targets reconstruction error against ground-truth images, while the resulting architecture is complex-valued rather than conventional real-valued.
II.B. Deep DNN for nonlinear EM inverse scattering
DeepNIS is a complex-valued deep network arranged as cascaded CNN modules for nonlinear EM inverse scattering. It begins with a BP image and successively transforms learned convolutional features through nonlinear and optional pooling operations.
- DeepNIS is a cascade of CNN modules whose first input is a BP image and whose later inputs are outputs from preceding modules.
- Each up-sampling convolution layer applies learned filters, a point-wise nonlinear function, and optionally pooling to form a multi-layer representation.
III. NUMERICAL AND EXPERIMENTAL RESULTS
The paper evaluates DeepNIS against conventional nonlinear inverse scattering methods using numerical and experimental demonstrations, with CSI included as a comparison method.
- The evaluation combines numerical and experimental demonstrations of DeepNIS for nonlinear electromagnetic inverse scattering.The discrete dipole method generates simulation data, while CSI provides the conventional nonlinear inverse-scattering comparison.
III.A Training and testing over MNIST dataset
DeepNIS is trained and tested on MNIST-based simulated scenes under a 2D MIMO measurement setup, then compared with BP and CSI using image-quality and timing measures.
- Training and testing over MNIST dataset: DeepNIS is trained and tested on the MNIST handwritten-digit dataset.The dataset contains ten handwritten digits, from 0 to 9.
- Measurement and simulation setup: The simulations use a 5.6×5.6λ0 square divided into 110×110 sub-squares, with 36 transmitters, 36 receivers, εr=3 objects, and 30 dB noise.
- Experimental configuration: The experimental setup uses a 5.6×5.6λ0 region discretized into 110×110 cells, with simulations performed using 36 transmitters and 36 receivers.
- Reconstruction comparison: DeepNIS reconstructions use one, two, or three CNN modules, while BP supplies the input and CSI serves as a comparison.
- Image quality: 2000 test images are evaluated with SSIM and MSE; two- or three-module DeepNIS results nearly match the ground truth.
- Computational time: Less than one second is required for a trained DeepNIS reconstruction, compared with about 8 seconds for BP and about 10 minutes for CSI.
III.B Testing over experimental data with trained networks
A network trained on MNIST is tested on Fresnel FoamDielExt experimental data with substantially different objects, producing satisfactory reconstructions and much shorter computation than CSI.
- Generalization: DeepNIS is tested on FoamDielExt experimental data after training exclusively on the MNIST dataset.
- Experimental target: The FoamDielExt target combines plastic with relative permittivity 3±0.3 and foam with relative permittivity 1.45 ± 0.15 at 4 GHz.
- Reconstruction quality: DeepNIS produces a satisfactory result comparable to CSI despite the experimental ground truth differing substantially from the training samples.
- Computational time: Around 1 second is needed for DeepNIS, whereas CSI takes several minutes and 70 iterations.
- Contrast regime: The experimental object has low dielectric contrast, within the reported range of validity of CSI.
III.C Testing over letter targets with trained networks
DeepNIS is evaluated on letter-shaped targets with relative permittivity 3 and is reported to outperform BP and CSI in reconstruction quality and imaging time.
- Test targets: The test objects are English letters with relative permittivity 3, while other parameters match the training dataset.
- Visual comparison: Figure 5 places ground truths in the first row and BP, CSI, and DeepNIS reconstructions in the second, third, and fourth rows.
- Imaging time: DeepNIS reconstruction takes less than 1 second, compared with about 8 seconds for BP and about 10 minutes for CSI.
- High-contrast reconstruction: Because the probed objects have large contrasts, CSI fails to provide acceptable images.
- Overall comparison: The results indicate that DeepNIS is markedly superior to BP and CSI in both imaging quality and imaging time.
- Generalization: Satisfactory reconstructions are obtained for objects very different from the MNIST training images, suggesting a generalizable mapping from BP results to inverse-scattering solutions.
IV. CONCLUSIONS
DeepNIS unfolds iterative nonlinear EM inverse scattering into a complex-valued CNN, enabling non-iterative parallel reconstruction. The authors report better image quality and computational time than conventional methods, with scope for large-scale and high-contrast objects.
- DeepNIS connects CNN architecture with an unfolded iterative solution for nonlinear EM inverse scattering.
- Its non-iterative and parallelizable convolution operations make DeepNIS suitable for large-scale inverse scattering problems.
- DeepNIS outperforms conventional inverse scattering methods in image quality and computational time.
- DeepNIS can learn the governing equations of the EM inverse scattering system when training and testing scenarios are similar.
- Complex-valued CNN module: A complex-valued CNN module contains up-sampling convolution, nonlinear activation, max-pooling, and up-sampling layers.
- Complex-valued CNN module: ReLU is applied separately to the real and imaginary parts because relative permittivity and conductivity are assumed non-negative.
APPENDIX B. MNIST DATASET
The numerical study uses MNIST handwritten-digit samples as probed objects in electromagnetic simulations. The objects are modeled as lossless dielectrics with relative permittivity 3.
- The numerical study models probed objects using MNIST, a widely used handwritten-digit dataset.
- The simulated objects are lossless dielectrics with relative permittivity 3.
- Some MNIST samples used in Figs.3-5 are shown in Fig. A2.