CAREER: Acquisition, Approximation, and Compression - An Integrated Study

该项目旨在开发新的数据采集算法，以减轻现实世界测量设备的基本限制。所有的测量设备在速度和定时精度上都是有限的。相应的主要目标是开发算法来补偿时间不准确的影响，并从缓慢采集的样本中有效地提取信息。这可以实现更便宜、更小、更低功耗的测量设备，从而加速大规模和电池供电传感系统的部署。磁共振成像（MRI）系统受到诱导磁激励均匀性的限制。第二个项目目标是在不增加激励时间的情况下优化激励序列的均匀性。这将使超高场核磁共振成像在临床和生理学研究中更有用，对医疗保健产生重大影响。技术进步的关键是仔细整合从近似和压缩到数据采集的工具。该研究计划还将辅以一本教科书、一门研究生课程，以及将在麻省理工学院开放课程软件和fourierandwavets.org上在线共享的材料。研究分为三个部分：(a)将开发用于减轻采样、量化数据抖动的算法。由于一些功耗与抖动的方差成反比，这些算法改进可以实现更低的功耗。该项目进一步寻求确定抖动影响的基本比例定律。(b)该项目处理来自少量（奈奎斯特以下）样本的信号估计。初步结果表明，近似理论和信息论对现有技术的有效性给出了截然不同的观点，新的获取和重建算法将被开发出来。(c) MRI激励设计是一个近似问题，适合基于稀疏性的优化

This project seeks to develop new algorithms for data acquisition that mitigate fundamental limitations in real-world measurement devices. All measurement devices are limited in their speed and timing accuracy. The corresponding primary goal is to develop algorithms to compensate for effects of timing inaccuracy and to extract information effectively from samples taken slowly. This could enable cheaper, smaller and lower-power measurement devices and thus hasten the deployment of large-scale and battery-operated sensing systems. Magnetic resonance imaging (MRI) systems are limited by the homogeneity of the induced magnetic excitation. A second project goal is to optimize excitation sequences for homogeneity without increase in excitation time. This would make ultra high-field MRI more useful clinically and in physiological research, with a significant impact on health care. Key to the technological advances is the careful integration of tools from approximation and compression into data acquisition. The research plan is complemented by the development of a textbook, a graduate course, and materials to be shared online at MIT Open Course Ware and FourierAndWavelets.org.The research has three parts: (a) Algorithms to mitigate jitter in sampled, quantized data will be developed. Since some power consumption is inversely proportional to the variance of jitter, these algorithmic improvements can enable lower power. The project further seeks to determine fundamental scaling laws for the effect of jitter. (b) The project addresses the estimation of signals from a small (sub-Nyquist) number of samples. Preliminary results demonstrate that approximation theory and information theory give quite different perspectives on the efficacy of existing techniques, and new acquisition and reconstruction algorithms will be developed. (c) MRI excitation design is posed as an approximation problem amenable to sparsity-based optimization