Sensing systems are found everywhere in the modern world, ranging from the microphones, video cameras, and antennas found in everyday cellular phones, to the radar systems used for astronomy, meteorology, archaeology, and defense applications, to the biomedical imaging systems used to understand the human body and its diseases. Real-world sensing systems must always strike a practical balance between the cost of data acquisition and the quality of the measured data. The costs of acquiring a large amount of high-quality data are prohibitive for many important applications, and place practical limits our ability to explore and understand our bodies, our world, and our universe. This effect is exacerbated as new sensors become increasingly capable of acquiring multidimensional data.
This research is focused on exploring the use of parsimonious low-rank signal models to extract information from incomplete and/or low-quality data. Specifically, the investigators are developing theory and methods to unify and generalize a range of existing constrained signal reconstruction methods within a framework based on low-rank matrix embeddings. While the new theory and methods can be applied in general sensing applications, the proposed models are being evaluated in the specific practical context of magnetic resonance imaging (MRI), where they can enable faster MRI experiments and more informative high-dimensional examinations.