Mapping of earth resources, environmental monitoring, and many other systems require high-resolution wide-area imaging. Since images often have to be captured at night or in inclement weather conditions, a capability is provided by Synthetic Aperture Radar (SAR). SAR systems exploit radar signal's long-range propagation and utilize digital electronics to process complex information, all of which enables high-resolution imagery. This gives SAR systems advantages over optical imaging systems, since, unlike optical imaging, SAR is effective at any time of day and in any weather conditions. Moreover, advanced technology called Interferometric Synthetic Aperture Radar (InSAR), has the potential to apply phase information from SAR images and to measure ground surface deformation. However, given the current state of technology, the quality of InSAR data can be distorted by several factors, such as image co-registration, interferogram generation, phase unwrapping, and geocoding. Image co-registration aligns two or more images so that the same pixel in each image corresponds to the same point of the target scene. Super-Resolution (SR), on the other hand, is the process of generating high-resolution (HR) images from a low-resolution (LR) one. SR influences the co-registration quality and therefore could potentially be used to enhance later stages of SAR image processing. Our research resulted in two major contributions towards the enhancement of SAR processing. The first one is a new learning-based SR model that can be applied with SAR, and similar applications. A second major contribution is utilizing the devised model for improving SAR co-registration and InSAR interferogram generation, together with methods for evaluating the quality of the resulting images. In the case of phase unwrapping, the process of recovering unambiguous phase values from a two-dimensional array of phase values known only modulo $2\pi$ rad, our research produced a third major contribution. This third major contribution is the finding that quantum annealers can resolve problems associated with phase unwrapping. Even though other potential solutions to this problem do currently exist - based on network programming for example - network programming techniques do not scale well to larger images. We were able to formulate the phase unwrapping problem as a quadratic unconstrained binary optimization (QUBO) problem, which can be solved using a quantum annealer. Since quantum annealers are limited in the number of qubits they can process, currently available quantum annealers do not have the capacity to process large SAR images. To resolve this limitation, we developed a novel method of recursively partitioning the image, then recursively unwrapping each partition, until the whole image becomes unwrapped. We tested our new approach with various software-based QUBO solvers and various images, both synthetic and real. We also experimented with a D-Wave Systems quantum annealer, the first and only commercial supplier of quantum annealers, and we developed an embedding method to map the problem to the D-Wave 2000Q_6, which improved the result images significantly. With our method, we were able to achieve high-quality solutions, comparable to state-of-the-art phase-unwrapping solvers. / Graduate