Coordination Funds

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，该定理确保以两倍带宽的采样率完全重建带限信号。相比之下，压缩感知遵循的范式是，一个稀疏的信号可能被采样到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突出的原则，稀疏性和非相干性。稀疏性指的是信号的信息速率远远小于其带宽的期望，因此信号可以由适当基或帧中的少量元素来表示。非相干表示具有稀疏表示的信号在采样域中分散的概念。在无线信息和通信技术、雷达监视、视觉和音频信号处理等众多应用中都会遇到稀疏性。在这个优先计划中，压缩感知在信息处理中的应用将被强调，然而，期望背后的数学理论将从应用问题中得到重大的影响和新的方向。特别鼓励工程师和应用数学家之间的配对合作项目。研究信号的稀疏性、带宽、动态和统计行为，通过压缩感知方法采样，以及原始信号的重建，构成了优先计划的重点。我们希望涵盖以下领域：•在压缩感知中使用统计先验信息•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补全•无线系统中的频谱传感•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•可视和音频信号处理除此之外，优先计划向可能有助于重点领域的建议和科学学科开放。

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.