Frame Theoretic Nonuniform Fast Fourier Transforms for Synthetic Aperture Imaging

Have you ever wondered how satellites can image your street from space? There's no way an optical camera could take pictures from that distance. How do they do it? Synthetic aperture radar (SAR). This processing technique - which can also be used to create detailed seafloor maps with sonar - allows for incredible ground resolution even when the imaging device is, well, in space. In my talk, I'll cover the basics of SAR image processing from a mathematical perspective and, additionally, I'll go through a technique I and some collaborators developed that works off of frame theory to improve a necessary inversion step from the Fourier to complex domain. This will require a little bit of linear algebra knowledge, but is a fun bit of numerical analysis with real-world relevance.