Exploiting Prior Knowledge in Compressed Sensing

智能优点：压缩传感(CS)领域有望给数字处理带来广泛的革命性变化。其关键思想是使用非自适应线性投影来直接使用几个测量来获得信号或图像的有效的降维表示。然而，当前实用的CS算法存在两个限制，这限制了它们在实际场景中的应用。首先，CS中的大部分工作都是处理确定性信号，并且不假设任何关于它们的先验知识。然而，在许多应用中，除了它们的稀疏性之外，关于潜在信号的附加先验信息也是可用的。先验信息可以是确定性的，也可以是统计的，例如通过二阶统计量。我们的初步结果表明，利用它可以显著提高性能。标准CS中的第二个限制是需要在感兴趣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。这项研究通过探索如何在CS的一般框架中使用先验信息来实现改进的性能来解决这些限制，即使在感兴趣的信号不允许稀疏表示的基础上执行重建也是如此。此外，作为概念验证，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和真实世界信号中的可行性。广泛影响：压缩传感方面的进展可能会产生广泛的深远影响，包括在光谱学、成像、通信以及消费电子领域的应用。该项目将包括一个综合教育项目，涉及两名博士生和三名本科生，他们将被引入这个新领域。

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.