Optimized sampling and processing of structured signals

结构化信号的优化采样和处理

• 批准号: 229268497
• 负责人: Dr.-Ing. Ullrich Mönich
• 金额: --
• 依托单位: Lehrstuhl für Theoretische Informationstechnik (LTI)
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/229268497?language=en
• 关键词: Optimized; sampling; processing; structured; signals

Today's information society is based on the power of digital signal processing, and the theoretical foundation for the digital processing of analog signals is the Shannon sampling theorem. Without any further information about bandlimited signals, Nyquist rate sampling is essentially optimal. However, if the signals have some additional structure-as is the case in many applications-it is possible to reduce the sampling rate below the Nyquist rate. The new field of compressed sensing provides a framework for sampling and recovering of sparse signals. However, sparsity is only one of many possible structures a signal can have. A specialized signal processing, including sampling, digital processing and subsequent reconstruction, that is adapted to the signal structure will lead to a post-Shannon sampling theory. Currently, it is not fully understood whether the new theory can replace the current standard theory, which has proven very useful but also shown to fail in several important cases, or if the new theory is an extension of the old one, so that the two theories complement each other. The goal of this project is to study the theoretical foundations of an adapted sampling, processing, and reconstruction for signals that have a specific structure. To this end, suitable signal spaces will be identified and new algorithms will be developed. The ideas of compressed sensing will be applied to more general signal classes, in particular to sparse analog signals, and used to develop new methods for system approximation. Further, practical applications and the influence of impairments like quantization and noise will be examined.

当今的信息社会基于数字信号处理的力量，而模拟信号的数字处理理论基础是香农采样定理。没有任何有关频带信号的进一步信息，nyquist速率采样实质上是最佳的。但是，如果信号具有一些额外的结构 - 在许多应用中是这种情况 - 可以将采样率降低到奈奎斯特率以下。新的压缩传感领域为稀疏信号采样和恢复提供了一个框架。但是，稀疏性只是信号可能具有的许多可能结构之一。适合信号结构的专门信号处理，包括采样，数字处理和随后的重建，将导致香农后抽样理论。目前，尚不完全了解新理论是否可以替换当前的标准理论，该理论被证明非常有用，但在几种重要情况下也证明是失败的，或者新理论是否是旧理论的扩展，因此两种理论相互补充。该项目的目的是研究具有特定结构的信号的适应性采样，处理和重建的理论基础。为此，将确定合适的信号空间，并将开发新的算法。压缩传感的想法将应用于更通用的信号类别，尤其是稀疏模拟信号，并用于开发系统近似的新方法。此外，将检查实际应用以及诸如量化和噪声等障碍的影响。

项目成果

A two channel approach for system approximation with general measurement functionals

• DOI: 10.1109/icassp.2015.7178698
• 发表时间: 2015-04
• 期刊: 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
• 作者: U. Mönich;H. Boche

Strong divergence for system approximations

• DOI: 10.1134/s0032946015030047
• 发表时间: 2015-05
• 期刊: Problems of Information Transmission
• 影响因子: 1.2
• 作者: H. Boche;U. Mönich

A signal model for forensic DNA mixtures

法医 DNA 混合物的信号模型

• DOI: 10.1109/acssc.2014.7094478
• 发表时间: 2014
• 期刊: 2014 48th Asilomar Conference on Signals, Systems and Computers
• 作者: Ullrich J. Mönich;Catherine Grgicak;Viveck Cadambe;Jason Yonglin Wu;Genevieve Wellner;Ken Duffy;Muriel Médard
• 通讯作者: Muriel Médard