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

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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