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Abstract Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to measurement arrays with reciprocally collocated transmitters and receivers, that is, square symmetric matrix (data) transfer functions. To relax this limitation, we use our previous work Druskin et al (2021 Inverse Problems 37 075003), where the ROMs were combined with the Lippmann–Schwinger integral equation to produce a direct nonlinear inversion method. In this work we extend this approach to more general transfer functions, including those that are non-symmetric, e.g., obtained by adding only receivers or sources. The ROM is constructed based on the symmetric subset of the data and is used to construct all internal solutions. Remaining receivers are then used directly in the Lippmann–Schwinger equation. We demonstrate the new approach on a number of 1D and 2D examples with non-reciprocal arrays, including a single input/multiple outputs inverse problem, where the data is given by just a single-row matrix transfer function. This allows us to approach the flexibility of the Born approximation in terms of acceptable measurement arrays; at the same time significantly improving the quality of the inversion compared to the latter for strongly nonlinear scattering effects.
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Reduced Order Modeling Inversion of Monostatic Data in a Multi-scattering Environment
Data-driven reduced order models (ROMs) have recently emerged as an efcient tool for the solution of inverse scattering problems with applications to seismic and sonar imaging. One requirement of this approach is that it uses the full square multiple-input/multiple-output (MIMO) matrixvalued transfer function as the data for multidimensional problems. The synthetic aperture radar (SAR), however, is limited to the single-input/single-output (SISO) measurements corresponding to the diagonal of the matrix transfer function. Here we present a ROM-based Lippmann-Schwinger approach overcoming this drawback. The ROMs are constructed to match the data for each source-receiver pair separately, and these are used to construct internal solutions for the corresponding source using only the data-driven Gramian. Efficiency of the proposed approach is demonstrated on 2D and 2.5D (3D propagation and 2D reflectors) numerical examples. The new algorithm not only suppresses multiple echoes seen in the Born imaging but also takes advantage of their illumination of some back sides of the reflectors, improving the quality of their mapping.
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- PAR ID:
- 10523656
- Publisher / Repository:
- SIAM
- Date Published:
- Journal Name:
- SIAM Journal on Imaging Sciences
- Volume:
- 17
- Issue:
- 1
- ISSN:
- 1936-4954
- Page Range / eLocation ID:
- 334 to 350
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1137/23M1564365
