Coordination Funds

协调基金

• 批准号: 282998623
• 负责人: Professorin Dr. Gitta Kutyniok
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/282998623?language=en
• 关键词: Coordination; Funds

Digital signal processing requires the conversion of analog signals in space and time to a discrete domain and vice versa. Conventional sampling relies on the Shannon Nyquist theorem which ensures complete reconstruction of a band limited signal by sampling at a rate twice the band-width. In contrast, compressed sensing follows the paradigm that a sparse signal may be sampled far below the Nyquist rate, but nevertheless may be completely recovered. Compressed sensing relies on two salient principles, sparsity and incoherence. Sparsity refers to the idea that the information rate of a signal is much smaller than expected from its bandwidth, so that the signal may be represented by a small number of elements in a proper basis or frame. Incoherence expresses the concept that signals with a sparse representation are spread out in the sampling domain. Sparsity is encountered in signals of numerous applications like wireless information and communication technology, radar surveillance, and visual and audio signal processing, to name a few. In this Priority Programme, applications of compressed sensing in information processing will be emphasised, however, it is expected that the mathematical theory behind will receive significant impact and new directions from applied issues. Paired cooperation projects between engineers and applied mathematicians are particularly encouraged. Investigating signals with respect to sparsity, bandwidth, dynamics, and statistical behaviour, sampling by compressed sensing methods, and reconstruction of the original signal forms the focus of the Priority Programme. We expect to cover the following areas: • using statistical prior information for compressed sensing • quantisation in compressed sensing • measurement design for compressed sensing • reconstruction algorithms for compressed sensing • low rank matrix recovery and matrix completion in signal processing Application fields of major interest include: • spectrum sensing in wireless systems • channel and network coding • signal processing in communications • radar and synthetic aperture radar imaging • visual and audio signal processing Beyond that the Priority Programme is open to proposals and scientific disciplines which may contribute to the focus areas.

数字信号处理需要将空间和时间上的模拟信号转换为离散域，反之亦然。传统的采样依赖于香农奈奎斯特定理，该定理通过以两倍带宽的速率采样来确保带限信号的完全重构。相比之下，压缩感知遵循的范式是稀疏信号可以远低于奈奎斯特速率进行采样，但仍然可以完全恢复。压缩感知依赖于两个突出的原则，稀疏性和非相干性。稀疏性是指信号的信息速率比其带宽所期望的要小得多，使得信号可以由适当的基或帧中的少量元素表示。非相干性表达了具有稀疏表示的信号在采样域中展开的概念。在诸如无线信息和通信技术、雷达监视以及视觉和音频信号处理等众多应用的信号中遇到稀疏性。在这个优先计划中，将强调压缩传感在信息处理中的应用，然而，预计背后的数学理论将受到重大影响，并从应用问题中获得新的方向。特别鼓励工程师和应用数学家之间的配对合作项目。优先方案的重点是调查信号的稀疏性、带宽、动态和统计特性，采用压缩传感方法进行采样，以及重建原始信号。我们预计将涵盖以下领域：·使用压缩感知的统计先验信息·压缩感知中的量化·压缩感知的测量设计·压缩感知的重建算法·信号处理中的低秩矩阵恢复和矩阵完成主要感兴趣的应用领域包括：·无线系统中的频谱感知·信道和网络编码·通信中的信号处理·雷达和合成孔径雷达成像·视频和音频信号处理除此之外，优先计划对可能有助于重点领域的建议和科学学科开放。