Project Details
Projekt
Exploiting structure in compressed sensing using side constraints – from analysis to system design (EXPRESS II)
Applicants
Professor Dr.-Ing. Martin Haardt; Professor Dr.-Ing. Marius Pesavento; Professor Dr. Marc Emanuel Pfetsch
Subject Area
Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
Mathematics
Mathematics
Term
from 2015 to 2023
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 273262315
In the first phase of the EXPRESS (Exploiting structure in compressed sensing using side constraints) project, we have investigated sparse signal recovery in the context of multidimensional frequency and direction-of-arrival estimation under various structural side constraints. We have devised new algorithms, optimization strategies, and theoretical results that exploit specific structures in the sensor array and the signal waveform to enhance sparse reconstruction. Building on the results obtained in the first phase, EXPRESS II (EXPRESS: From analysis to system design – funding phase II) shifts the focus towards the design of cost efficient analog-digital acquisition systems for sparse signals under structure.Modern large-scale hybrid analog/digital multi-antenna arrays and hardware architectures for compressed sensing involve analog mixing networks composed of low-end low-cost hardware components and low resolution baseband sampling units replacing traditional architectures with costly individual per-antenna high-end transceiver chains. The network performs a linear transformation of the sensor measurements in space, frequency, and time using configurable radio frequency (RF) components and maps them to a reduced number of outputs connected to low-cost transceiver chains (down-converter, power-amplifiers, sampling units, . . . ) with generally nonlinear characteristics.The key objective in EXPRESS II is to design, configure, and dimension the hybrid analog/digital data acquisition system for sparse signal recovery under structure. In accordance with EXPRESS I, we consider exploiting prior knowledge of particular structure in the array geometry (e.g., uniform-linear arrays, shift-invariant arrays, . . . ), the source signals (e.g., signal constellations, constant modulus, . . . ), and the temporal signature of the signals (e.g., block-, row-, or rank-sparsity) in the hybrid system. In our design, we address the fundamental questions of how to synthesize the analog mixing network (dimension of the mixing networks, filter weights, etc.), and how to choose and parameterize nonlinear network components, e.g., for thresholding or quantization to sense the signal most efficiently in terms of hardware cost and storage bandwidth, given the prior knowledge that the signal exhibits sparsity in some domain. This requires theoretical results regarding the sparse signal recoverability exploiting the available structure as well as formulating and solving the corresponding optimization criteria. Considering the concept of virtual array design, we enforce favorable structures for sparse reconstruction. Moreover, with respect to sparse signals with structure, we explore the potential to improve recoverability using methods from mixed-integer nonlinear programming. Finally, we address row-, block- and rank-sparse recovery from nonlinear mixtures exploiting temporal structure and high-dimensional data.
DFG Programme
Priority Programmes
