CIF: Small: Collaborative Research: Design and Analysis of Novel Compressed Sensing Algorithms via Connections with Coding Theory

CIF：小型：协作研究：通过与编码理论的联系设计和分析新型压缩感知算法

• 批准号: 1344364
• 负责人: Georgios-Alex Dimakis
• 金额: $ 19.66万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-01-16 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1344364&HistoricalAwards=false
• 关键词: CIF; Small; Collaborative; Research; Design

Compressed sensing (CS) is a rapidly advancing area of signal processing and statistics that has the potential to radically change the way that analog signals are transformed into digital signals. The main idea is to acquire a sparse signal from a very small number of measurements using a specialized sampling and reconstruction process. Since one promising application of CS is medical imaging, improvements in CS systems are also expected to advance real-world healthcare applications. In this project, the investigators will study the fundamental connection between error-correcting codes (ECC) and CS and leverage recent advances in ECC to design improved CS measurement and reconstruction systems.In particular, the connection between linear-programming (LP) decoding of binary linear codes and LP reconstruction will be used to develop a non-asymptotic theory for the design and analysis of CS algorithms and measurement matrices. The first part of the project will focus on novel relaxations of the CS reconstruction problem that allow non-convex regularization and iterative solution. The second part of the project will focus on applying the theory of pseudo-codewords, which was originally developed to understand iterative and LP decoding of binary linear codes, to achieve a non-asymptotic analysis of iterative reconstruction algorithms for CS. The third part of the project will focus on exploiting additional signal structure (i.e., beyond sparsity) that exists in high-contrast imaging applications such as angiograms.

压缩传感（CS）是信号处理和统计数据的快速前进的领域，有可能从根本上改变模拟信号转换为数字信号的方式。 主要思想是使用专门的采样和重建过程从少量测量中获取稀疏信号。 由于CS的有希望的应用是医学成像，因此CS系统的改进也有望推进现实世界中的医疗保健应用。 在该项目中，研究人员将研究错误纠正验证的代码（ECC）与CS之间的基本联系，并利用ECC的最新进展，以设计改进的CS测量和重建系统。尤其是，线性编程（LP）解码的二进制线性代码和LP重建者的连接将用于开发非序列的分析和分析，并进行分析，并进行了分析，并设计了COTOITY的理论。矩阵。 该项目的第一部分将集中于CS重建问题的新放松，该问题允许非凸正则化和迭代解决方案。 该项目的第二部分将着重于应用伪代码理论，该理论最初是为了了解二进制线性代码的迭代和LP解码，以实现CS迭代重建算法的非反应分析。 该项目的第三部分将集中于利用在高对比度成像应用（例如血管造影）中存在的其他信号结构（即超出稀疏性）。