Exploiting Prior Knowledge in Compressed Sensing

利用压缩感知的先验知识

• 批准号: 0725422
• 负责人: Javier Garcia-Frias
• 金额: $ 30万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0725422&HistoricalAwards=false
• 关键词: Exploiting; Prior; Knowledge; Compressed; Sensing

Intellectual Merit: The field of compressive sensing (CS) promises to revolutionize digital processing broadly. The key idea is the use of nonadaptive linear projections to acquire an efficient, dimensionally reduced representation of a signal or image directly using just a few measurements. However, there are two limitations in current practical CS algorithms that constrain their application in practical scenarios. First, most of the work in CS deals with deterministic signals and does not assume any prior knowledge about them. In many applications, however, additional a priori information on the underlying signals is available, in addition to their sparsity. The a priori information may come either deterministically or statistically, e.g., through second order statistics. Our preliminary results show that exploiting it leads to a substantial performance improvement. The second constraint in standard CS is the need to perform reconstruction in a basis where the signal of interest admits a sparse representation, which reduces flexibility in practical applications. This research addresses these limitations by exploring how a priori information can be used in the general framework of CS to achieve improved performance, even when reconstruction is performed in a basis where the signal of interest does not admit a sparse representation. Furthermore, as a proof of concept, we will build a hardware demonstration system to show the feasibility of the proposed techniques in practical CS and with real-world signals.Broader Impact: Advances in compressive sensing may have a profound impact broadly, including applications in spectroscopy, imaging, communications, as well as consumer electronics. This project will include an integrated educational program involving two Ph.D. students and three undergraduate students, who will be introduced into this new field.

智力优势：压缩传感 (CS) 领域有望彻底改变数字处理。 关键思想是使用非自适应线性投影，仅使用少量测量即可直接获取信号或图像的高效、降维表示。 然而，当前实用的CS算法存在两个局限性，限制了其在实际场景中的应用。 首先，计算机科学的大部分工作都涉及确定性信号，并且不假设任何有关它们的先验知识。 然而，在许多应用中，除了稀疏性之外，还可以获得有关底层信号的附加先验信息。 先验信息可以是确定性的或统计性的，例如通过二阶统计。 我们的初步结果表明，利用它可以显着提高性能。 标准CS的第二个约束是需要在感兴趣的信号允许稀疏表示的基础上执行重建，这降低了实际应用中的灵活性。 本研究通过探索如何在 CS 的通用框架中使用先验信息来解决这些限制，以实现改进的性能，即使是在感兴趣的信号不允许稀疏表示的基础上执行重建时也是如此。 此外，作为概念证明，我们将构建一个硬件演示系统，以展示所提出的技术在实际 CS 和现实世界信号中的可行性。 更广泛的影响：压缩传感的进步可能会产生广泛的深远影响，包括在光谱学、成像、通信以及消费电子产品。 该项目将包括一个涉及两名博士的综合教育计划。学生和三名本科生，他们将被引入这个新领域。