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[ספר][B] Geometric inverse problems
GP Paternain, M Salo, G Uhlmann - 2023 - books.google.com
This up-to-date treatment of recent developments in geometric inverse problems introduces
graduate students and researchers to an exciting area of research. With an emphasis on the …
graduate students and researchers to an exciting area of research. With an emphasis on the …
Inverting the local geodesic X-ray transform on tensors
We prove the local invertibility, up to potential fields, and stability of the geodesic X-ray
transform on tensor fields of order 1 and 2 near a strictly convex boundary point, on …
transform on tensor fields of order 1 and 2 near a strictly convex boundary point, on …
On an inverse boundary value problem for a nonlinear elastic wave equation
We consider an inverse boundary value problem for a nonlinear elastic wave equation
which was studied in [1]. We show that all the parameters appearing in the equation can be …
which was studied in [1]. We show that all the parameters appearing in the equation can be …
Integral geometry on manifolds with boundary and applications
4 Integral geometry on manifolds with boundary and applications Page 1 Joonas Ilmavirta
and François Monard 4 Integral geometry on manifolds with boundary and applications …
and François Monard 4 Integral geometry on manifolds with boundary and applications …
Lens rigidity for manifolds with hyperbolic trapped sets
For a Riemannian manifold $(M, g) $ with strictly convex boundary $\partial M $, the lens
data consist of the set of lengths of geodesics $\gamma $ with end points on $\partial M …
data consist of the set of lengths of geodesics $\gamma $ with end points on $\partial M …
The geodesic X-ray transform with matrix weights
Consider a compact Riemannian manifold of dimension $\geq 3$ with strictly convex
boundary, such that the manifold admits a strictly convex function. We show that the …
boundary, such that the manifold admits a strictly convex function. We show that the …
Travel time tomography
We survey some results on travel time tomography. The question is whether we can
determine the anisotropic index of refraction of a medium by measuring the travel times of …
determine the anisotropic index of refraction of a medium by measuring the travel times of …
Reconstruction and interpolation of manifolds. I: The geometric Whitney problem
We study the geometric Whitney problem on how a Riemannian manifold (M, g) can be
constructed to approximate a metric space (X, d_X)(X, d X). This problem is closely related to …
constructed to approximate a metric space (X, d_X)(X, d X). This problem is closely related to …
A minicourse on microlocal analysis for wave propagation
This minicourse describes a microlocal framework for the linear analysis that has been
useful for the global understanding of wave propagation phenomena. While it is useful to …
useful for the global understanding of wave propagation phenomena. While it is useful to …
Deep learning architectures for nonlinear operator functions and nonlinear inverse problems
We develop a theoretical analysis for special neural network architectures, termed operator
recurrent neural networks, for approximating nonlinear functions whose inputs are linear …
recurrent neural networks, for approximating nonlinear functions whose inputs are linear …