CAREER: Robust Methods for High-Dimensional Signal Processing under Geometric Constraints

我们的社会正在见证一场由数据驱动的改革浪潮，这些改革在许多方面对我们的生活产生了积极影响，这要归功于技术的进步，使医学和生物成像、社交和无线传感器网络、物联网、推荐系统等领域的新型数据采集模式成为可能。然而，越来越多的大量数据是以不可靠和校准不良的方式获取的，这使得难以利用现有方法将其转化为可用于决策的知识。这个CAREER项目的目标是开发一个统一的框架，包括设计可证明的鲁棒性和有效的算法，表征的基本限制，在各种实际考虑因素下的信号重建，如不完美的校准，传感器漂移，互耦，腐败和数据采集过程中丢失的数据。该项目的成功将对传感和成像科学的许多应用产生深远的影响。这个CAREER项目将建立在信号处理的最新进展，利用低维几何约束作为之前正则化，否则不适定的推理问题。引入自校准模型，其中传感器扰动被建模为需要与感兴趣的信号同时恢复的未知量。变换方面是认识到扰动还表现出低维几何结构，其应当以与感兴趣的信号的低维几何结构集成的方式被利用，以呈现适定的推断问题，从而实现自校准。职业计划将通过为各级学生开发量身定制的教育组件，设计适合传播给K-12学生的信号处理模块，并让妇女和代表性不足的学生参与进来，通过推广活动促进他们的成功，来推进STEM教育。

Our society is witnessing a surge of data-driven reforms that positively impact our lives in many aspects, thanks to technology advances that enable novel data acquisition modalities in medical and biological imaging, social and wireless sensor networks, internet-of-things, recommendation systems and so on. However, increasingly the large volume of data is acquired in an unreliable and poorly-calibrated manner, making it difficult to translate into actionable knowledge for decision making using existing methodologies. The objective of this CAREER project is to develop a unified framework, including design of provably robust and efficient algorithms, characterization of the fundamental limits, for signal reconstruction under a variety of practical considerations such as imperfect calibrations, sensor drifts, mutual coupling, corruptions and missing data during data acquisition. The success of this project will have far-reaching impacts on many applications in sensing and imaging science. This CAREER project will build upon recent advances in signal processing that exploit low-dimensional geometric constraints as a prior to regularize an otherwise ill-posed inference problem. Self-calibration models are introduced where the sensor perturbation is modeled as an unknown that needs to be recovered simultaneously with the signal of interest. The transformative aspect is to recognize that the perturbation also exhibits low-dimensional geometric structures, which shall be exploited in an integrated manner with the low-dimensional geometric structure of the signal of interest to render a well-posed inference problem to enable self-calibration. The CAREER program will advance STEM education by developing tailored educational components for students at all levels, designing signal processing modules that are appropriate for dissemination to K-12 students, and involving women and underrepresented students to promote their success through outreach activities.