The problem of computing a Fourier representation of data is a fundamental one, that arises in many areas of mathematics, science, and technology. Recently, a class of algorithms has been proposed to approximate the Fourier transform, with provable quality guarantees, in dramatically less time than required by traditional exact algorithms. The investigator and his colleagues evaluate competing variations of the algorithm, both proposed and new, and choose the best from among them for general purpose use as well as for specific application to Magnetic Resonence Imaging and solution of partial differential equations, including advection-diffusion equations.
The Fourier Transform is a fundamental technique with many applications. The investigator and his team investigate recent approximate methods that are dramatically more efficient than traditional methods. The team directly addresses applications to biomedical Magnetic Resonance Imaging and the modeling of liquid and gas behavior, which has further applications to studying the atmosphere and bodies of water in the environment, as well as applications to manufacturing. The investigator and his team also make available fundamental tools that will be useful to others in a broad range of scientific, educational, and engineering settings including modeling the interactions of tiny particles, reliable telecommunications, and imaging generally. The project combines cutting-edge techniques from several disciplines and trains a graduate student in these techniques and their integration.
