For inverse problems in imaging, deep learning has become a powerful tool to overcome challenges such as incomplete model knowledge arising in physically challenging acquisition environments, and generating compressive representations of image manifolds to tackle conventionally ill-posed problems efficiently. Our research has focused on utilizing deep learning in conjunction with physics-based modeling to capture the underlying sensing processes governed by inverse scattering theory toward developing foundations for the black-box nature of high-complexity models via the end-to-end design of reconstruction methods. Our research to this end encompasses a wide range of inverse problems in acoustic, geophysical, and electromagnetic imaging such as blind deconvolution, target recognition, imaging in multiple scattering environments, imaging dynamic scenes, passive sensing, and synthetic aperture imaging. 

In this direction, our ongoing research goal is conforming deep learning with physics-based signal models from inverse scattering theory, towards developing foundations of physics-aware learning for performance guarantees for computational sensing and addressing ill-posed inverse problems in imaging. 

Passive sensing is an exciting paradigm with growing interest due to cost, stealth, resource efficiency, and flexibility benefits. With the increasing amount of sources and demand in the EM spectrum, leveraging passive sensing enables the development of novel imaging systems that can co-exist with the next generation of communication and IoT networks. One of the most powerful computational tools to this end is interferometry which utilizes cross-correlation measurements acquired from sensors configured in space, time, or frequency and has found crucial use in a wide range of applications including astronomical, electromagnetic, acoustic, seismic, and medical imaging. Conventional passive imaging is based on Fourier inversion, which relies on certain simplifying assumptions of spatial incoherence and can only recover up to partial information on the unknown of interest.

Novel theory, methods, and algorithms are of great importance for the development of next-generation imaging systems that are highly sought after by defense agencies, and industry in health-care, and communication networks. Our ongoing goals include addressing increasingly challenging sample-starved regimes and mitigating the effects of model errors that arise due to unknowns in the propagation environment.

Non-convex optimization has become a major area of advancement due to its computational efficiency in recovering low-rank models, which arise in problems across many disciplines including imaging, remote sensing, data science, and training deep neural networks. Despite the conventional challenges of non-convex optimization, there has been considerable success in developing provably good methods in the last decade based on novel algorithmic principles with results that reveal a benign global geometry under certain conditions. The development of novel theoretical conditions and analysis for the reliable use of non-convex optimization in the recovery of low-rank models continues to be an essential research area with an impact on a plethora of applications in optics, material science, quantum computing, medicine, defense & security, and robotics.

Our research goals in this area have been dedicated to establishing deterministic recovery guarantees of computationally efficient, first-order methods that iterate using the original low-rank factored forms, and solving quadratic inverse problems with performance guarantees applicable to inverse scattering models encountered in imaging applications.

Manifold optimization methods have a growing interest in signal processing and imaging applications toward the advancement of key computational methods in MIMO systems such as space-time adaptive signal processing, constant false-alarm rate detection, hybrid beamforming in dual function radar-communication systems,  localization & target detection, passive source localization to name a few with close relationship to distributed imaging and computational techniques such as interferometry in multi-static imaging and distributed sensor configurations. On the other hand information geometry is an essential tool for tasks such as clustering, variational inference, and probability density estimation which have close interplay with problems such as phaseless imaging due to the shared manifold of positive measures. 

Our research goal in this area is to leverage the data structure of imaging systems to advance the performance and robustness of reconstruction methods using fundamental theory from information geometry, and methods & algorithms developed from the foundations of manifold optimization. 

Wave-based imaging modalities use back-scattered fields from electromagnetic, acoustic, or seismic sources of illumination to recover the underlying scattering profile for imagery. The sensing procedure is effectively modeled by k-space samples arising from wave-matter interaction and propagation models from inverse scattering theory. Conventional wave-based imaging systems in medical, remote sensing, and geophysical applications rely on phase information of scattering fields for synthetic aperture formation and inversion of the k-space samples coherently. However coherent processing is susceptible to propagating small phase errors to significant errors in the reconstructed images. This is especially challenging for large-scale distributed imaging systems that need to be precisely calibrated and phase-synchronized to leverage spatial diversity via conventional coherent processing techniques.

Our research in this area has been dedicated to the development of phaseless synthetic aperture formation techniques and performance guarantees based on theoretical, methods, and algorithms from low-rank-matrix-recovery theory to enable large-scale distributed imaging systems, with extended impact on mm-wave & THz imaging in the next-generation wireless networks, medical ultra-sound, optical tomography, radar & sonar imaging. 

One of the most challenging problems in synthetic aperture imaging is the localization and tracking of moving targets. Imaging modalities such as synthetic aperture radar use the relative motion of the antenna with respect to a stationary scene to generate high-resolution imagery via conventional Fourier inversion techniques applied over a coherent processing interval. The presence of moving targets and dynamics in the scene of interest violates the core assumptions of synthetic aperture formation, introducing major artifacts and potential limitations in the resolution of synthetic aperture imaging systems. Motion in the scene introduces spatially varying, velocity-dependent range variations which must be corrected for accurate parameter estimation, image refocusing, and tracking of key targets of interest. Such tasks have a wide range of impact with applications in communication networks, autonomous systems, environmental monitoring, and defense & security. 

Our research in this area has been dedicated to developing super-resolution techniques that are capable of off-grid localization and point estimation of motion parameters, using state-of-the-art computational tools from semidefinite programming, compressed sensing, and optimization theory for application to ground moving target imaging in synthetic aperture radar.