CIF: Medium: Collaborative Research: Subspace Matching and Approximation on the Continuum

在各种各样的应用领域--包括天文成像、显微镜、无线通信、雷达、声纳等--人们必须面对从由少量未知（连续值）参数控制的信号中估计或提取信息的问题。针对这些应用中的每一个，过去已经提出了处理这些未知参数的独特方法。这项研究涉及到一个统一的框架的发展，以解决所有这些领域的问题，系统，有效，与意识的基本限制，并证明准确性。第一个组成部分涉及模型的发展，其中感兴趣的信号位于或接近于一个子空间或子空间的并集。在信号的基本参数是连续值的情况下，这是一个具有挑战性的任务。而不是简单地诋毁这些问题（一个程序可能fraughtwith困难），这项研究涉及到一个本地无限范围的子空间使用有效的本地子空间适合其尺寸匹配的effectivennumber的本地自由度的finiteapproximations的发展。这个框架的第二个组成部分包括用于识别负责从一组离散观测值生成信号的子空间范围的技术，面对由相干性、参数空间的连续性以及某些信号可以从窄的观测值合成的事实所带来的困难。这些组件联合收割机使得能够有效地获取，处理，以及由参数化子空间模型产生的信号估计。

In a diverse range of application areas--including astronomicalimaging, microscopy, wireless communications, radar, sonar, andmany others--one must confront the problem of estimating orextracting information from a signal that is governed by a smallnumber of unknown (continuous-valued) parameters. Customized toeach of these applications, unique methods for handling theseunknown parameters have been proposed in the past. This researchinvolves the development of a unified framework for addressingproblems in all of these areas systematically, efficiently, withawareness of the fundamental limits, and with provable accuracy.There are two main components of this framework. The firstcomponent involves the development of models where the signals ofinterest lie within or close to a subspace or a union of subspaces.In the case where the underlying parameters for the signal arecontinuous-valued, this is a challenging task. Rather than attemptto simply discredit these problems (a program potentially fraughtwith difficulty), this research involves the development of finiteapproximations for a locally infinite range of subspaces usingefficient local subspace fits whose dimensions match the effectivenumber of local degrees of freedom. The second component of thisframework consists of techniques for identifying the range ofsubspaces responsible for generating a signal from a set ofdiscrete observations, confronting difficulties posed by thecoherence, by the continuous nature of the parameter space, and bythe fact that some signals may be synthesized from a narrow (butcontinuously-indexed and therefore infinite) range of subspaces.These components combine to enable the efficient acquisition,processing, and estimation of signals arising from theparameterized subspaces model.