This grant supports a collaborative team of researchers from Arizona State University and the Keller Center for Imaging Innovation at the Barrow Neurological Institute. The research team consists of five mathematical scientists, representing complementary expertise in pure and applied harmonic analysis, computational mathematics, and statistics, and two experts in Magnetic Resonance Imaging (MRI). The project highlights scientific challenges in the domain of MR data acquisition and reconstruction, including image formation from sparse and/or non-uniformly collected data, restoration of data corrupted by system imperfections, as well as rapid and robust image construction from data acquired by multiple receivers. The crosscutting expertise of the research team is enabling development of rigorous tools for addressing these challenges, providing the underpinnings for provable results, quantifiable measures of performance, and efficient algorithms. The team's approach entails in-depth mathematical study of data collection procedures utilized in MRI, including the physical constraints under which they must be undertaken. This understanding provides the basis for conceptualization, analysis, implementation, and validation of accurate, efficient and effective practical algorithms for processing imaging data. A particular emphasis of the project is unification of the data collection and image generation aspects of MRI, which are often considered independently even by informed researchers. Methodology is sought to enable joint design of acquisition and post-processing techniques that can optimally serve medical requirements. In particular, this research aims to facilitate design of data post-processing methods that are fully informed about the characteristics of the raw sensor data, such as its non-uniformly sampled spectral nature and underlying statistical variations.
The activities of the collaborative research team from Arizona State University and the Barrow Neurological Institute (BNI) are expected to have significant impact on strengthening the mathematical foundations of magnetic resonance imaging (MRI). The project focuses several areas of applicable mathematics on a circle of application problems where the introduction of improved mathematical techniques offers potential for substantial performance improvements. These, in turn, will ultimately have broad social impact by improving the fidelity of medical diagnoses, decreasing the cost of medical tools that are presently very expensive, and alleviating patient discomfort by decreasing imaging time and the need for patients to remain motionless for extended periods for accurate imaging. Broader impact will be realized through the connections of the planned research to other application areas, such as synthetic aperture radar, where algorithmic challenges in acquisition and post-processing are similar to those in MRI. Aligned with the research program is a plan for integration of educational components which includes support of undergraduate and graduate students, as well as the design of new courses. Junior participants will be provided with the modern mathematical training which is needed for their later pursuit of cross-disciplinary cutting-edge professional careers.
