Electromagnetic inverse scattering problems (ISPs) have led to many ground-breaking imaging technologies in a wide range of fields, including medical imaging, remote sensing, nondestructive testing of mechanical structures, security scanners, sub-atomic microscopy, and astronomical imaging. Conventional techniques to solve electromagnetic ISPs are limited in terms of the size (in terms of wavelengths) and relative permittivity of objects that can be reconstructed. In addition, these techniques need both magnitude and phase measurements of the wave field scattered by the target objects. However, it is often difficult to obtain accurate phase measurements, especially in high-frequency imaging applications. For such applications, ISPs need to be solved with phaseless data, which results in...[ Read more ]

Electromagnetic inverse scattering problems (ISPs) have led to many ground-breaking imaging technologies in a wide range of fields, including medical imaging, remote sensing, nondestructive testing of mechanical structures, security scanners, sub-atomic microscopy, and astronomical imaging. Conventional techniques to solve electromagnetic ISPs are limited in terms of the size (in terms of wavelengths) and relative permittivity of objects that can be reconstructed. In addition, these techniques need both magnitude and phase measurements of the wave field scattered by the target objects. However, it is often difficult to obtain accurate phase measurements, especially in high-frequency imaging applications. For such applications, ISPs need to be solved with phaseless data, which results in a highly non-linear, non-convex, and severely ill-posed inverse problem. As a result, existing phaseless inverse scattering techniques have not found practical applications in large-scale microwave imaging applications such as indoor imaging, where scattering can be extremely strong, and the collection of accurate phase data is not practically feasible.

This thesis presents new linear phaseless inverse scattering techniques that have a range of validity (in terms of object size and permittivity) far beyond existing techniques. These techniques are also implementable in terms of computation, measurement collection, and handling of experimental errors and are therefore extremely useful in many practical ISP settings. These techniques are based on the well-known Rytov Approximation (RA), which is a linear approximation to the underlying non-linear inverse problem and can be used with phaseless data. However, RA has a small validity range and fails under strong scattering conditions. To increase the validity range, crucial corrections to RA are derived using a high-frequency theory of inhomogeneous wave propagation in strongly scattering, lossy media. This corrected RA is denoted as the extended phaseless Rytov approximation for lossy media (xPRA-LM), and it is the basis for the phaseless inverse scattering techniques proposed in this work.

This thesis is divided into six chapters. Chapter 1 provides a literature survey on existing inverse scattering techniques and also on the existing Wi-Fi-based indoor imaging techniques. Chapter 2 provides mathematical and physical preliminaries and ISP formulation in the context of a Wi-Fi-based indoor imaging setup. The proposed corrections to RA and derivation of the xPRA-LM model are provided in Chapter 3, along with the demonstration of imaging accuracy of xPRA-LM in the indoor environment. Chapter 4 extends the inverse xPRA-LM model to formulate a new non-iterative linear technique to solve the forward scattering problem. Chapter 5 incorporates the well-known distorted wave iterative framework with xPRA-LM model to achieve improved performance. Finally, in Chapter 6, the proposed techniques are further verified for 1D fault imaging in transmission lines, followed by the conclusions.

Using extensive simulations and experiments for the use case of indoor imaging (using phaseless Wi-Fi signals), the proposed techniques are shown to surpass the state-of-the-art validity range by a significant margin. The proposed techniques are shown to provide an accurate reconstruction of objects up to relative permittivity values of 15 + 1.5j for object sizes greater than 30 wavelengths. Even at higher relative permittivity values of up to ϵ_r = 77+7j, object shape reconstruction remains accurate; however, the reconstruction amplitude is less accurate. To the best of our knowledge, no other existing phaseless inverse scattering techniques work under such extremely strong scattering conditions. Therefore, the proposed linear phaseless techniques can pave the way for using the theory of phaseless inverse scattering in practical microwave and radio imaging applications which was not possible before.