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

该项目寻求开发新的数据采集算法，以缓解真实世界测量设备的基本限制。所有的测量设备在速度和计时精度方面都是有限的。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。这可以使更便宜、更小和更低功率的测量设备成为可能，从而加快大规模电池供电的传感系统的部署。磁共振成像(MRI)系统受到诱导磁激励的均质性的限制。第二个项目目标是在不增加激发时间的情况下优化激发序列的同质性。这将使超高场磁共振在临床和生理研究中更有用，对医疗保健产生重大影响。技术进步的关键是将从近似和压缩到数据采集的工具仔细地整合在一起。作为对研究计划的补充，该研究计划开发了一本教科书、一门研究生课程，以及将在麻省理工学院公开课Ware和傅立叶和小波网站上在线共享的材料。研究包括三个部分：(A)将开发减少采样、量化数据中抖动的算法。由于一些功耗与抖动的变化成反比，因此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效果的基本比例律。(B)该项目涉及从少量(低于奈奎斯特的)样本中估计信号。初步结果表明，近似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)将核磁共振激励设计假设为服从稀疏性优化的逼近问题

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