# Reduced order model approach for imaging with waves

@article{Borcea2021ReducedOM, title={Reduced order model approach for imaging with waves}, author={Liliana Borcea and Josselin Garnier and Alexander V. Mamonov and J{\"o}rn T. Zimmerling}, journal={ArXiv}, year={2021}, volume={abs/2108.01609} }

We introduce a novel, computationally inexpensive approach for imaging with an active array of sensors, which probe an unknown medium with a pulse and measure the resulting waves. The imaging function uses a data driven estimate of the “internal wave” originating from the vicinity of the imaging point and propagating to the sensors through the unknown medium. We explain how this estimate can be obtained using a reduced order model (ROM) for the wave propagation. We analyze the imaging function… Expand

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SHOWING 1-10 OF 21 REFERENCES

A Nonlinear Method for Imaging with Acoustic Waves Via Reduced Order Model Backprojection

- Physics, Mathematics
- SIAM J. Imaging Sci.
- 2018

A novel nonlinear imaging method for the acoustic wave equation based on model order reduction that resolves all the dynamical behavior captured by the data, so the error from the imperfect knowledge of the velocity model is purely kinematic. Expand

Robust nonlinear processing of active array data in inverse scattering via truncated reduced order models

- Physics, Mathematics
- J. Comput. Phys.
- 2019

A novel algorithm for nonlinear processing of data gathered by an active array of sensors which probes a medium with pulses and measures the resulting waves, based on a reduced order model defined by a proxy wave propagator operator that has four important properties. Expand

Untangling the nonlinearity in inverse scattering with data-driven reduced order models

- Mathematics
- 2018

The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the… Expand

Reduced Order Model Approach to Inverse Scattering

- Computer Science, Physics
- SIAM J. Imaging Sci.
- 2020

A novel inversion method, based on a reduced order model (ROM) of an operator called wave propagator, because it maps the wave from one time instant to the next, at interval corresponding to the discrete time sampling of the data, is introduced. Expand

Direct, Nonlinear Inversion Algorithm for Hyperbolic Problems via Projection-Based Model Reduction

- Mathematics, Computer Science
- SIAM J. Imaging Sci.
- 2016

This work estimates the wave speed in the acoustic wave equation from boundary measurements by constructing a reduced-order model (ROM) matching discrete time-domain data and presents results of inversion experiments for one- and two-dimensional synthetic models. Expand

Synthetic Aperture Radar

- Physics
- IEEE Transactions on Aerospace and Electronic Systems
- 1967

The general theory of side-looking synthetic aperture radar systems is developed. A simple circuit-theory model is developed; the geometry of the system determines the nature of the prefilter and the… Expand

3D Seismic Imaging

- Computer Science
- 2006

This book introduces wavefield-continuation imaging methods by leveraging the intuitive understanding gained during the study of integral methods, and discusses the relationships between imaging methods and acquisition geometries throughout the text. Expand

Wave Propagation and Time Reversal in Randomly Layered Media

- Materials Science
- 2007

and Overview of the Book.- Waves in Homogeneous Media.- Waves in Layered Media.- Effective Properties of Randomly Layered Media.- Scaling Limits.- Asymptotics for Random Ordinary Differential… Expand

Mathematical and Statistical Methods for Multistatic Imaging

- Mathematics
- 2013

Mathematical and Probabilistic Tools.- Small Volume Expansions and Concept of Generalized Polarization Tensors.- Multistatic Configuration.- Localization and Detection Algorithms.- Dictionary… Expand

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

- Mathematics, Medicine
- Proceedings of the National Academy of Sciences
- 2016

This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning and using sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. Expand