
Reduced order models for spectral domain inversion: Embedding into the continuous problem and generation of internal data
We generate datadriven reduced order models (ROMs) for inversion of the...
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Reduced Order Model Approach to Inverse Scattering
We study an inverse scattering problem for a generic hyperbolic system o...
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A theory of consciousness: computation, algorithm, and neurobiological realization
The most enigmatic aspect of consciousness is the fact that it is felt, ...
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Inverse conductivity equation with internal data
This paper concerns the reconstruction of a scalar coefficient of a seco...
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Inversion formula with hypergeometric polynomials and its application to an integral equation
For any complex parameters x and ν, we provide a new class of linear inv...
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Differential tomography of micromechanical evolution in elastic materials of unknown micro/macrostructure
Differential evolution indicators are introduced for 3D spatiotemporal i...
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A WeakForm Combined Source Integral Equation with Explicit Inversion of the CombinedSource Condition
The combined source integral equation (CSIE) for the electric field on t...
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LippmannSchwingerLanczos algorithm for inverse scattering problems
Datadriven reduced order models (ROMs) are combined with the LippmannSchwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a Galerkin projection and is sparse due to Lanczos orthogonalization. Embedding into the continuous problem, a datadriven internal solution is produced. This internal solution is then used in the LippmannSchwinger equation, thus making further iterative updates unnecessary. We show numerical experiments for spectral domain domain data for which our inversion is far superior to the Born inversion and works as well as when the true internal solution is known.
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