Project Details
Projekt
Coordination Funds
Applicants
Professorin Dr. Gitta Kutyniok; Professor Dr. Holger Rauhut, since 8/2019
Subject Area
Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
Mathematics
Mathematics
Term
from 2015 to 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 282998623
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.
DFG Programme
Priority Programmes
Ehemaliger Antragsteller
Professor Dr. Rudolf Mathar, until 7/2019
