Electromagnetic inverse scattering problems (ISPs) involve accurately modeling the scattering of waves to infer the shape and constitution of objects. These problems can be found in various forms in a wide range of research and commercial applications including medical imaging, remote sensing, microscopy, security scanners, non-destructive evaluation and many more. Such inverse problems can be highly nonlinear and severely ill-posed under strong scattering conditions such as when the target objects have very high permittivity or are electrically large. The extent of non-linearity and ill-posedness can increase further if the measurements of scattered waves do not contain phase information.

State-of-the-art model-based approaches to solve such ISPs rely on the underlying physics-based fo...[ Read more ]

Electromagnetic inverse scattering problems (ISPs) involve accurately modeling the scattering of waves to infer the shape and constitution of objects. These problems can be found in various forms in a wide range of research and commercial applications including medical imaging, remote sensing, microscopy, security scanners, non-destructive evaluation and many more. Such inverse problems can be highly nonlinear and severely ill-posed under strong scattering conditions such as when the target objects have very high permittivity or are electrically large. The extent of non-linearity and ill-posedness can increase further if the measurements of scattered waves do not contain phase information.

State-of-the-art model-based approaches to solve such ISPs rely on the underlying physics-based formulations and non-linear optimization techniques. However, such model-based techniques have a limited validity range due to the high non-linearity and severe ill-posedness of ISPs and do not provide accurate reconstructions for objects with large size and high permittivity.

In recent years, deep learning-based methods have been employed to solve such problems. The success of these methods relies on the ability of deep networks to learn highly non-linear functions and intricate relationships, which is not possible with traditional model-based methods. However, these methods rely on the use of large amounts of training data to obtain accurate solutions, without which they fail to generalize successfully. This dependence on a large amount of training data makes purely deep learning-based methods impractical for use in a lot of scenarios where collecting data is difficult and expensive. The interpretability of deep learning methods has also not been fully understood.

This thesis presents two model-based deep learning frameworks, which combine physics model-based techniques with deep learning in order to overcome the drawbacks of each of these and extend the validity range of both. Such frameworks exploit the domain knowledge available through physics-based models, while at the same time leveraging the deep networks to learn additional information from the training data available. Using physics-based models in the framework reduces the reliance of deep networks on training data, and the resulting model-based deep learning frameworks need much less data to obtain accurate solutions to ISPs as compared to purely deep learning-based methods.

The performance of these frameworks is demonstrated on the use case of indoor imaging using simulations and experiment results in actual indoor environments using 2.4 GHz Wi-Fi phaseless measurements. Using model-based deep learning frameworks leads to a remarkable increase in the validity range over existing state-of-the-art linear and non-linear model-based methods, and accurate reconstructions are obtained for objects with very high relative permittivity (│∈_r│≤77) and electrical size almost 20 times larger than the probing wavelength.

This thesis is divided into five chapters. Chapter 1 provides the background on electromagnetic inverse scattering problems and on the different types of deep learning techniques used to solve such inverse problems. Chapter 2 provides the formulation of ISPs in the context of a Wi-Fi-based indoor imaging setup. Chapters 3 and 4 demonstrate the use of two different model-based deep learning frameworks to solve the ISPs for the indoor imaging use case, followed by the conclusion in Chapter 5.