Project Details
Projekt
Bilinear Compressed Sensing - Efficiency, Structure, and Robustness
Subject Area
Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
Mathematics
Mathematics
Term
from 2015 to 2022
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 273529854
Practical data acquisition processes often rely on uncalibrated systems. This is a natural source of bilinear compressed sensing problems. These are problems, where the measurement outcomes depend linearly on both the signal and the calibration parameters. If one uses traditional Compressed Sensing (CS) schemes for such bilinear problems, one needs to operate at sub-optimal sensing rates or incur significant reconstruction errors due to model mismatch.For this reason, work on a theoretical foundation of such "blind information retrieval problems" has started over the past years, partly in the context of our project in the first phase of the priority program. In many cases, it has been established that these problems can indeed have tractable solutions. These first results, however, were still somewhat removed from being applicable in practice. The goal of our project will be to close this gap by developing theory for bilinear compressed sensing that better addresses issues arising in applications. In this vein, we have identified the following challenges that will serve as a guiding theme for our project. (1) Efficiency: Design and analyze algorithms that can cope with real-world problem sizes. This will frequently necessitate going beyond the framework of convex optimization. (2) Structure: Rely less on highly randomized constructions that are typically comparativelysimple to analyze mathematically, but often impractical to implement.(3) Robustness: Focus on the ability of reconstruction algorithms to withstand theimpact of noise and model mismatch present in real-world applications.
DFG Programme
Priority Programmes
