DeepNIS: Deep Neural Network for Nonlinear Electromagnetic Inverse Scattering (1810.03990v1)

Abstract: 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.

• The paper introduces DeepNIS, a novel deep neural network leveraging complex-valued residual CNNs to address the challenges of nonlinear electromagnetic inverse scattering.
• DeepNIS significantly outperforms conventional methods like CSI, demonstrating superior image quality and computational efficiency, particularly for high-contrast, large-scale scenes.
• This non-iterative, DNN-based approach offers practical advantages for real-time applications and holds implications for fields like biomedical imaging and non-destructive testing.

DeepNIS: Advancing Nonlinear Electromagnetic Inverse Scattering Using Deep Neural Networks

The paper presents a significant development in the field of nonlinear electromagnetic (EM) inverse scattering by introducing a novel deep neural network-based methodology, termed DeepNIS. Nonlinear EM inverse scattering is renowned for its ability to provide quantitative and super-resolution images of internal structures, accounting for complex interactions between EM wavefields and the scene's structure. However, the challenges inherent in this technique largely stem from its strong nonlinearity, ill-posed nature, and high computational demands.

Overview of Contributions

The authors establish a connection between deep neural network (DNN) architectures and iterative methods for nonlinear EM inverse scattering, facilitating the development of DeepNIS. This approach leverages a cascade of multi-layer complex-valued residual convolutional neural network (CNN) modules, which approximate the multi-scattering physical mechanism in the scattering scene. This characteristic sets DeepNIS apart from traditional solving methods, which are often computationally expensive and limited in scope, particularly at high frequencies and with high-contrast objects.

Key Findings

Through extensive numerical simulations and experimental validations, DeepNIS is demonstrated to outperform conventional nonlinear inverse scattering methods, both in terms of image quality and computational efficiency. Specifically, the methodology shows significant advantages in processing scenes with large size and high contrast—problems traditionally deemed impractical for existing techniques. DeepNIS is validated using the MNIST dataset, as well as experimental data from the Fresnel dataset, confirming its robust generalization capabilities.

Experimentation and Results

The DeepNIS's performance is substantiated by training and testing on datasets involving digit-like and letter-shaped dielectric objects. The paper reports that DeepNIS significantly improves reconstruction quality over established methods like the contrast source inversion (CSI) method. The use of metrics such as Structural Similarity Index Measure (SSIM) and Mean-Square Error (MSE) objectively quantifies these improvements, with DeepNIS achieving higher SSIM scores and lower MSE values. Notably, while the CSI method struggles with high-contrast scenarios leading to inadequate reconstructions due to powerful multi-scattering effects, DeepNIS continues to deliver high-quality images.

The non-iterative nature of DeepNIS translates into reduced computational burdens, with the paper citing substantially decreased processing times—underscoring the practical applicability of the method in real-time and resource-constrained environments. Furthermore, it takes advantage of deep learning’s ability to learn intricate mappings, facilitating its application to complex nonlinear EM inverse scattering problems.

Future Directions and Implications

The insights provided by this research lay the groundwork for future explorations into more advanced DNN architectures, which could further enhance imaging quality and expand the applicability of EM inverse scattering methods. The strength of DeepNIS in addressing the computational challenges associated with large-scale, nonlinear problems suggests broad implications for fields such as biomedical imaging, non-destructive testing, and remote sensing.

In conclusion, this paper is a substantial addition to the arsenal of inverse scattering techniques, positioning DNN-based approaches as formidable solutions to longstanding challenges in nonlinear EM inverse scattering. The proposed framework not only offers improved results but also paves the way for exploring the adaptation of similar neural network-based approaches to other complex scientific domains.