CAREER: Practical Compressive Signal Processing

“信号”是想要获取的任何数据集，例如，图像、大块数据或音频片段。可以想象，询问需要多快地对音频片段进行采样，以便仅从这些样本就可以准确地恢复音频片段。您需要每纳秒、每毫秒还是每秒采样一次？压缩信号处理（CSP）表明，许多信号中的重要信息可以从比传统认为的少得多的样本中获得和恢复。CSP的应用非常广泛，包括成像（医学，高光谱，显微镜，生物学），模拟到信息转换，雷达，大规模信息合成，地球物理数据分析，计算生物学等等。尽管这些应用令人震惊，但CSP的理论工作与CSP在实际环境中的使用之间存在脱节。该项目的目标将通过提供适用于真实世界信号和设置的CSP方法和分析来弥合这一差距。这些工作将导致减少MRI的扫描时间，降低计算基础设施的成本和能耗，改进从高光谱图像中检测病害作物，提高雷达的准确性，并改进许多其他大数据应用中的压缩和分析。此外，该项目将涉及各级学生，并向他们介绍严格的科学研究。PI积极从代表性不足的人群中招募成员，并将继续通过她自己的研究和推广计划促进多样性。早期的CSP模型将信号的类别限制为在非常特定的意义上（相对于正交或不相干基础的稀疏）可压缩的信号。这个项目的一个目标是放松这个限制，以允许在实践中实际遇到的信号，如那些稀疏的冗余，连贯，和高度过完备的字典。我们将利用贪婪方法和基于优化的方法，针对特定的字典，以及更一般的方法，为任意基地。此外，该项目还将开发自适应CSP采样方案，其中信号的测量是在进行测量时“动态”设计的。传统的测量方案忽略了这些信息，而自适应方案有可能显着减少重建误差，测量次数和计算时间。我们将确定约束和无约束设置的最佳测量策略，并从信息论的角度分析实际上可以从自适应性中获得多少。该项目还将涉及“一位CSP”的工作，这是CSP的一个新的令人兴奋的分支，可以处理极端（通常更现实）的量化。我们将利用次线性方法，其中大的误差自然出现，并且还使用基于优化的技术沿着自适应量化阈值，以将恢复误差降低到非自适应量化的最佳可能值以下。在研究这些主题时，本研究将弥合CSP理论中的巨大差距，并为实践者和研究者提供一个统一的框架。

A "signal" is any data set that one would like to acquire, for example, an image, a large block of data, or an audio clip. One can imagine asking how quickly one would need to sample an audio clip so that from those samples alone, the audio clip could be accurately recovered. Would you need to sample every nanosecond, every millisecond, or every second? Compressive Signal Processing (CSP) shows that the important information in many signals can be obtained and recovered from far fewer samples than traditionally thought. The applications of CSP are widespread and include imaging (medical, hyperspectral, microscopy, biological), analog-to-information conversion, radar, large scale information synthesis, geophysical data analysis, computational biology, and many more. Although these applications are astounding, there has been a disconnect between the theoretical work in CSP and the use of CSP in practical settings. The goals of this project will bridge this gap by providing methods and analysis for CSP that apply to real-world signals and settings. Such work will lead to decreased scan time in MRI, reduced cost and energy consumption in computing infrastructures, improved detection of diseased crops from hyperspectral images, increased accuracy in radar, and improved compression and analysis in many other large-data applications. In addition, this project will involve students at all levels and introduce them to rigorous scientific research. The PI actively recruits members from under-represented populations, and will continue to promote diversity through her own research and outreach programs.Early CSP models restrict the class of signals to those compressible in a very specific sense (sparse with respect to an orthonormal or incoherent basis). One goal of this project is to relax this restriction to allow for signals actually encountered in practice, such as those sparse in redundant, coherent, and highly overcomplete dictionaries. We will utilize both greedy approaches and optimization-based methods, tailored to specific dictionaries of interest, as well as more general methods for arbitrary bases. In addition, this project will develop adaptive CSP sampling schemes, where measurements of the signal are designed "on the fly," as they are being taken. Traditional measurement schemes ignore this information, while adaptive schemes have the potential to significantly reduce reconstruction error, number of measurements, and computation time. We will identify optimal measurement strategies for constrained and unconstrained settings, and analyze how much one can actually gain from adaptivity from an information theoretic point of view. The project will also involve work in "one-bit CSP", a new and exciting branch of CSP which handles extreme (and often more realistic) quantization. We will draw on sub-linear methods, where large errors appear naturally, and also use optimization based techniques along with adaptive quantization thresholds to reduce the recovery error below the best possible for non-adaptive quantization. In studying these topics, the research will bridge a large gap in the theory of CSP and provide a unified framework for both practitioners and researchers.