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

Abstract

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 inversion is to determine from these measurements the structure of the scattering medium, modeled by a spatially varying acoustic impedance function. Many inversion algorithms assume that the mapping from the unknown impedance to the scattered waves is approximately linear. The linearization, known as the Born approximation, is not accurate in strongly scattering media, where the waves undergo multiple reflections before they reach the sensors in the array. Thus, the reconstructions of the impedance have numerous artifacts. The main result of the paper is a novel, linear-algebraic algorithm that uses a reduced order model (ROM) to map the data to those corresponding to the single scattering (Born) model. The ROM construction is based only on the measurements at the sensors in the array. The ROM is a proxy for the wave propagator operator, that propagates the wave in the unknown medium over the duration of the time sampling interval. The output of the algorithm can be input into any off-the-shelf inversion software that incorporates state of the art linear inversion algorithms to reconstruct the unknown acoustic impedance.

arXiv comment27 pages, 9 figures

References in corpus (5)

• Detection and imaging in a random medium: A matrix method to overcome multiple scattering and aberration
• A model reduction approach to numerical inversion for a parabolic partial differential equation
• Direct, nonlinear inversion algorithm for hyperbolic problems via projection-based model reduction
• A nonlinear method for imaging with acoustic waves via reduced order model backprojection
• Multi-scale S-fraction reduced-order models for massive wavefield simulations

Cited by in corpus (6)

• Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems
• Robust nonlinear processing of active array data in inverse scattering via truncated reduced order models
• Reduced order model approach for imaging with waves
• On extension of the data driven ROM inverse scattering framework to partially nonreciprocal arrays
• Resolving Full-Wave Through-Wall Transmission Effects in Multi-Static Synthetic Aperture Radar
• Reduced Order Modeling for First Order Hyperbolic Systems with Application to Multiparameter Acoustic Waveform Inversion