CAREER: Geometric Techniques for Big Data Medical Imaging

医学成像极大地受益于信号和图像处理的进步，这使得更好的数据采集、更好的重建和对大量成像数据的改进分析成为可能。随着分辨率的提高和全面诊断的推动，医学成像面临新的挑战；包括更大的数据大小、更长的扫描持续时间以及对诸如患者运动等人为因素的易感性。因此，在存在系统和生理缺陷，以及对诊断能力和患者吞吐量的限制的情况下，对这些大规模数据集进行有效的处理和分析是势在必行的。该项目建立了一个跨学科的研究框架，提供基于几何方法的理论、算法和应用发展，以表征极限，并改善医学成像重建和分析的状态。本研究包括三个互补的重点：学习算法的速率失真表征；低维模型相位恢复的理论保证与算法以及一类参数估计问题在低维流形上的优化策略。这些重点都与医学成像的应用相辅相成，在美国医疗保健系统中具有巨大的转化影响潜力，包括提高医疗保健应用中的诊断和吞吐量。本项目将研究与研究生和本科课程相结合，从而产生更广泛的教育影响；向当地社区和贫困的K-12学生伸出援手。

Medical imaging has benefited greatly from advances in signal and image processing, which have enabled better data acquisition, superior reconstruction and improved analysis of massive amounts of imaging data. With improving resolutions and the push for comprehensive diagnosis, medical imaging faces new challenges; including bigger data sizes, longer scan durations, and susceptibility to artifacts, such as patient motion. Hence, it is imperative that these large-scale datasets are processed and analyzed efficiently in the presence of systematic and physiological imperfections, along with constraints on diagnostic ability and patient throughput.This project builds a cross-disciplinary research framework to provide theoretical, algorithmic and application developments based on geometric methods to characterize the limits and to improve the state of medical imaging reconstruction and analysis. This research comprises three complementary thrusts: rate-distortion characterization of learning algorithms; theoretical guarantees and algorithms for phase retrieval of low-dimensional models; and optimization strategies on low-dimensional manifolds for a class of parameter estimation problems. Each of these thrusts is complemented with applications in medical imaging, with tremendous potential for translational impact in the US healthcare system, including improved diagnosis and throughput in health-care applications. Broader educational impacts of this project result from integration of the research to graduate and undergraduate curriculum; outreach to the local community and to under-privileged K-12 students.