Structured compressed sensing algorithms: design, analysis and applications

科学和工程中的许多问题需要从测量集合中重建对象--例如，图像、信号或高维函数。由于时间、成本或其他方面的限制，人们往往受到可收集的数据量的严重限制，这严重影响了人们准确恢复未知对象的能力。本研究项目涉及基于压缩感知(CS)理论和技术的针对该问题的新算法的开发、分析和应用。相关应用的例子包括医学成像、显微镜、物理系统中的不确定性量化、机器学习和偏微分方程组的数值解。它的首要目标是为这类应用引入新的、计算高效的数值优化技术，这些技术既具有更高的精度，又具有较低的获取时间和成本。

Many problems in science and engineering require the reconstruction of an object - an image, signal or high-dimensional function, for example - from a collection of measurements. Due to time, cost or other constraints, one is often severely limited by the amount of data that can be collected, which significantly affects ones ability to recover the unknown object accurately. This research program involves the development, analysis and application of new algorithms for this problem, based on the theory and techniques of compressed sensing (CS). Examples of relevant applications include medical imaging, microscopy, uncertainty quantification in physical systems, machine learning and the numerical solution of PDEs. Its overarching objective is to introduce new, computationally-efficient numerical optimization techniques for such applications that possess both better accuracy and lower acquisition time and cost.