Coordination Funds

数字信号处理需要将空间和时间上的模拟信号转换到离散域，反之亦然。传统的采样依赖于香农·奈奎斯特定理，该定理通过以两倍于带宽的速率采样来确保完全重构带宽受限的信号。相反，压缩感知遵循这样的范例，即稀疏信号的采样可能远低于奈奎斯特速率，但仍然可以完全恢复。压缩感知依赖于两个显著的原则：稀疏性和不一致性。稀疏性指的是信号的信息速率远小于其带宽的预期，从而信号可以由适当的基数或帧中的少量元素来表示。不一致性表示具有稀疏表示的信号在采样域中展开的概念。稀疏性在许多应用中都会遇到，比如无线信息和通信技术、雷达监视以及视频和音频信号处理，仅举几例。在这一优先计划中，将强调压缩传感在信息处理中的应用，但预计其背后的数学理论将受到重大影响，并将从应用问题中获得新的方向。工程师和应用数学家之间的配对合作项目尤其受到鼓励。调查信号的稀疏性、带宽、动力学和统计行为、采用压缩感测方法进行采样以及重建原始信号是优先方案的重点。我们期望涵盖以下领域：·将统计先验信息用于压缩感知·在压缩感知中进行量化·用于压缩感知的测量设计·用于压缩感知的重构算法·信号处理中的低阶矩阵恢复和矩阵补全·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·优先方案对可能有助于重点领域的提案和科学学科开放。

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.