Support: US Air Force Office of Scientific Research (AFOSR)

Period of Performance: May 15, 2024 — September 30, 2027

Budget: $780,000

Summary:  The main goal is to build and test a robust methodology for mitigating the distortions of space-borne synthetic aperture radar (SAR) images due to the ionospheric turbulence. While turbulence in the Earth’s ionosphere has been known as a detriment to SAR for years, no comprehensive remedy has been proposed to date. The variational algorithm of transionospheric autofocus introduced in our recent work holds a substantial promise for correcting the image distortions in a variety of challenging spaceborne SAR scenarios. In the course of the project, we will conduct a thorough analysis of transionospheric autofocus and further develop it into a dependable and universal image correcting procedure using both traditional and data-driven approaches. The proposed development of transionospheric autofocus will include extending its focusing ability to a broad range of potential targets (beyond point scatterers), as well as to the scenarios with high levels of turbulent fluctuations. A detailed study is warranted of the various models for the Earth’s ionosphere, as well as various cost functions for optimization that characterize how sharp the image is. Finding the right balance between the quality of transionospheric SAR reconstruction and its cost will also be important. The optimization problem associated with transionospheric autofocus is often non-convex and non-smooth, which makes it difficult to solve. This problem merits a thorough analysis from two different perspectives. On one hand, we can modify the formulation in a way that would not substantially alter the minimization landscape yet make it more easily amenable to gradient-based optimizers. On the other hand, non-gradient optimization algorithms (and/or random algorithms) may prove a viable alternative for finding the global minimum in the non-convex/non-smooth situation. We also plan to consider a deep learning reformulation of transionospheric autofocus. The case of point scatterers is easier and may thus be better suited for network training. Once the network has been trained, it can be applied to distributed targets and the resulting focusing capacity can be evaluated. This approach is known as generalization. Its advantage is that deep learning may alleviate the difficulty of constructing the direct focusing metrics for distributed targets, which is harder than for point scatterers. Our additional goals are the analysis of SAR targets, as well as the extraction of the regions of interest from SAR images by means of machine learning. Beyond the classification of targets into instantaneous and delayed in 1D and in 2D, other scenarios may include multiple targets of various types, targets that are both dispersive in time and distributed in space, textured background, etc. The quantification of scattering delay is another worthwhile objective, as well as the application of artificial neural networks to the analysis of moving targets. Finally, a data-driven approach can be helpful for the extraction of the regions of interest. The latter can first be extracted from low resolution images. Then, one can change the imaging mode and generate high-resolution images of those smaller regions of interest from the newly acquired data.