Project Details
Projekt
Structured Compressive Sensing via Neural Network Learning (SCoSNeL)
Applicants
Professor Dr. Giuseppe Caire, Ph.D., since 8/2019; Professor Dr. Holger Rauhut
Subject Area
Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
Mathematics
Mathematics
Term
from 2018 to 2023
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 404374102
Compressed sensing predicts that signals from low complexity classes such as sparse vectors or low rank matrices can be recovered from an incomplete set of (random) linear measurements via efficient algorithms such as l1-minimization. Deep neural networkshave been very successful for various classification and regression tasks in recent years. In this joint project between two groups in mathematics and electrical engineering at RWTH Aachen, we will investigate whether deep neural networks can be trained to reconstruct signals in general low complexity classes from incomplete linear measurements. First empirical investigations on the standard class of sparse vectors are very promising. It seems very interesting to find out whether neural networks can adapt to rather general signal classes that may be unknown a-priori by training on sample signals from the class. We will investigate this approach for the recovery of signals from compressed measurements systematically both empirically (numerically) as well as on a theoretical level. Important questions concern the minimal number of linear measurements required to reconstruct signals and the number of training samples that ensure to train a correspondingneural network decoder. In addition to the reconstruction task, we will also investigate classification and regression directly on the compressed measurements using learned networks and whether this requires only a reduced number of measurements compared to the reconstruction problem. We will first investigate such questions for the standard case of random Gaussian matrices and pass then to structured random matrices such as partial random circulant matrices and random partial Fourier matrices. Finally, we will study recovery from nonlinear measurements.
DFG Programme
Priority Programmes
Ehemaliger Antragsteller
Professor Dr. Rudolf Mathar, until 7/2019
