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CORDIS

Signals, Waves, and Learning: A Data-Driven Paradigm for Wave-Based Inverse Problems

Project description

Theory combined with experience keep scattering algorithms on track

Imagine a cue ball struck in the first play of a pool game, traveling with significant kinetic energy toward the rest of the balls huddled en masse awaiting their fate. These balls scatter upon impact in ways that can be predicted readily given all the physical parameters of the system such as masses, friction coefficients, and velocity vectors. Scattering of energetic waves in other situations due to imperfections in the medium of transmission can be much more complicated; however, accurate prediction is fundamental to tasks in fields from biomedicine to seismology. The EU-funded SWING project plans to boost the power of scattering computational algorithms by combining theoretical approaches with data-driven (deep learning) ones while defining the limits of each.

Objective

Scattering of waves governs fundamental questions in science, from imaging molecules to fine-tuning concert hall acoustics. Efficient scattering computations rely on sparse representations of wavefields. Spurred by the empirical successes of deep learning, the emphasis has recently shifted to data-driven modeling. However, unlike signal-theoretic implementations that come with sharp approximation guarantees, it remains unclear whether the popular deep learning structures can represent important scattering operators.

In SWING, we address this question by leveraging advances in signal processing and machine learning. We propose theory and algorithms for the upcoming, learning-based wave of breakthroughs in forward and inverse scattering. SWING is built on three research thrusts:
1. To design efficient computational structures with approximation guarantees for learning scattering operators. We will focus on minimal structures for Fourier integral operators which model key problems.
2. To treat learning for inverse scattering as a sampling problem and derive practical sample complexity results. We will explore connections between learning theory and stability of inverse problems, and examine the regularization roles of data, physics and nonlinearity.
3. To apply our techniques to two classes of inverse problems: (i) emerging modalities in molecular imaging, giving rise to problems in geometry and unlabeled sampling; and (ii) seismic tomography of Earth and Mars, with data-driven discretizations of scattering operators playing a central role.

With the growth of wave-based sensing, there is an urgency to quantify the limits of the data-driven paradigm in scattering problems. The power of data in fitting models is indisputable: it is certainly the next frontier. We believe, however, that the best designs combine data-based models with an understanding of the underlying physics.

Host institution

UNIVERSITAT BASEL
Net EU contribution
€ 1 986 430,00
Address
PETERSPLATZ 1
4051 Basel
Switzerland

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Region
Schweiz/Suisse/Svizzera Nordwestschweiz Basel-Stadt
Activity type
Higher or Secondary Education Establishments
Links
Total cost
€ 1 986 430,00

Beneficiaries (1)