CAREER: Low-Rank Matrix Modeling for Constrained Reconstruction from Noisy and Sparsely-Sampled Data

传感系统在现代世界随处可见，从日常手机中的麦克风、摄像机和天线，到用于天文、气象、考古和国防应用的雷达系统，再到用于了解人体及其疾病的生物医学成像系统。真实世界的传感系统必须始终在数据采集成本和测量数据质量之间取得实际平衡。获取大量高质量数据的成本对于许多重要的应用程序来说是令人望而却步的，而且实际情况限制了我们探索和理解我们的身体、我们的世界和我们的宇宙的能力。随着新的传感器获取多维数据的能力越来越强，这种影响会加剧。本研究的重点是探索使用简约的低阶信号模型来从不完整和/或低质量的数据中提取信息。具体地说，研究人员正在开发理论和方法，以在基于低阶矩阵嵌入的框架内统一和推广一系列现有的约束信号重构方法。虽然新的理论和方法可以应用于一般的传感应用，但所提出的模型正在磁共振成像(MRI)的特定实践背景下进行评估，在那里它们可以实现更快的MRI实验和更具信息量的高维检查。

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.