Unique continuation of the normal operator of the x-ray transform and applications in geophysics

DOI10.1088/1361-6420/ab6e75zbMath1477.44002arXiv1909.05585OpenAlexW3002711191WikidataQ108775020 ScholiaQ108775020MaRDI QIDQ5000588

Joonas Ilmavirta, Keijo Mönkkönen

Publication date: 14 July 2021

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.05585

zbMATH Keywords

inverse problemsunique continuationnormal operatortheoretical seismologyx-ray tomography

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Inverse problems in geophysics (86A22) Radon transform (44A12)

Related Items (7)

Partial data problems and unique continuation in scalar and vector field tomography ⋮ Unique continuation results for certain generalized ray transforms of symmetric tensor fields ⋮ Fractional Calderón problems and Poincaré inequalities on unbounded domains ⋮ On determining and breaking the gauge class in inverse problems for reaction-diffusion equations ⋮ The fractional \(p\)-biharmonic systems: optimal Poincaré constants, unique continuation and inverse problems ⋮ Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems ⋮ X-ray Tomography of One-forms with Partial Data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ten equivalent definitions of the fractional Laplace operator
• A support theorem for the geodesic ray transform on functions
• Support theorems for real-analytic Radon transforms
• An example of non-uniqueness for generalized Radon transform
• Inverting the local geodesic X-ray transform on tensors
• Tensor tomography in periodic slabs
• Integral geometry for tensor fields. Transl. from the Russian
• The fractional Calderón problem: low regularity and stability
• Strong unique continuation for the higher order fractional Laplacian
• Travel time tomography
• The geodesic ray transform on Riemannian surfaces with conjugate points
• The inverse problem for the local geodesic ray transform
• The Mathematics of Computerized Tomography
• Microlocal Analysis in Tomography
• Stability of the interior problem with polynomial attenuation in the region of interest
• Integral Geometry and Radon Transforms
• Singularities of the X-Ray Transform and Limited Data Tomography in $\mathbb{R}^2 $ and $\mathbb{R}^3 $
• 4. Integral geometry on manifolds with boundary and applications
• Solving the interior problem of computed tomography usinga prioriknowledge
• High-order total variation minimization for interior tomography
• Abel transforms with low regularity with applications to x-ray tomography on spherically symmetric manifolds
• On local tomography
• Wavelet methods for a weighted sparsity penalty for region of interest tomography
• Mixed ray transform on simple 2-dimensional Riemannian manifolds
• Unique Continuation for Fractional Schrödinger Equations with Rough Potentials
• Long-wave elastic anisotropy produced by horizontal layering
• Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations
• Distributions, partial differential equations, and harmonic analysis

This page was built for publication: Unique continuation of the normal operator of the x-ray transform and applications in geophysics