Invertibility and stability for a generic class of Radon transforms with application to dynamic operators

DOI10.1515/jiip-2018-0014zbMath1429.44001arXiv1707.08936OpenAlexW2951593635WikidataQ128813788 ScholiaQ128813788MaRDI QIDQ2316698

Siamak Rabieniaharatbar

Publication date: 6 August 2019

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.08936

zbMATH Keywords

pseudodifferential operatorsFourier integral operatorsBolker condition

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Radon transform (44A12) Pseudodifferential and Fourier integral operators on manifolds (58J40) Integral geometry (53C65)

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Using the Navier-Cauchy equation for motion estimation in dynamic imaging, An efficient reconstruction approach for a class of dynamic imaging operators, Microlocal Properties of Dynamic Fourier Integral Operators

Cites Work

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• The X-ray transform for a generic family of curves and weights
• A support theorem for the geodesic ray transform on functions
• Support theorems for real-analytic Radon transforms
• Local tomography for the limited-angle problem
• Stability estimates for the \(X\)-ray transform of tensor fields and boundary rigidity
• Injectivity and stability for a generic class of generalized Radon transforms
• Reconstruction of dynamic objects with affine deformations in computerized tomography
• Fourier integral operators. I
• Microlocal Analysis in Tomography
• Local Tomography and the Motion Estimation Problem
• Detectable Singularities from Dynamic Radon Data
• Motion compensated local tomography
• An accurate approximate algorithm for motion compensation in two-dimensional tomography
• The inversion problem and applications of the generalized radon transform
• Some Problems in Integral Geometry and Some Related Problems in Micro-Local Analysis
• Improved cone beam local tomography
• Efficient algorithms for linear dynamic inverse problems with known motion
• Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients