The Reshetnyak formula and Natterer stability estimates in tensor tomography

DOI10.1088/1361-6420/33/2/025002zbMath1362.65139OpenAlexW2565137333MaRDI QIDQ2965684

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Publication date: 3 March 2017

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

Full work available at URL: https://semanticscholar.org/paper/6170044762c79a33427dbbd42c221edb131398d2

zbMATH Keywords

Radon transformPlancherel formulatensor tomographystability estimatesReshetnyak formulax-ray transform

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Radon transform (44A12) Numerical methods for integral transforms (65R10)

Related Items

Ray transform on Sobolev spaces of symmetric tensor fields. I: Higher order Reshetnyak formulas ⋮ The stability estimates of the inverse problem for the weighted Radon transform ⋮ Functional Relations, Sharp Mapping Properties, and Regularization of the X-Ray Transform on Disks of Constant Curvature ⋮ New approximate inverse results for the attenuated Radon transform with complex-valued coefficients ⋮ X-ray transform on Sobolev spaces ⋮ Stability estimates in tensor tomography ⋮ Radon transform on Sobolev spaces ⋮ On the approximate inverse method in SPECT image reconstruction ⋮ Injectivity and Range Description of Integral Moment Transforms Over $m$-Tensor Fields in $\mathbb{R}^n$

Cites Work

• The Cauchy problem for hyperbolic equations not resolved with respect to the highest time derivative
• Approximate inverse and Sobolev estimates for the attenuated Radon transform
• Practical and mathematical aspects of the problem of reconstructing objects from radiographs
• The finite element method for ill-posed problems