Structured compressed sensing algorithms: design, analysis and applications

科学和工程中的许多问题都需要从一组测量数据中重建对象，例如图像、信号或高维函数。由于时间，成本或其他限制，人们往往受到可以收集的数据量的严重限制，这严重影响了准确恢复未知对象的能力。该研究计划涉及开发，分析和应用新的算法解决这个问题，基于压缩传感（CS）的理论和技术。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的数值解。其总体目标是为这些应用引入新的，计算效率高的数值优化技术，这些应用具有更好的精度和更低的采集时间和成本。

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.