Two simple shearlet-based inverses for the multidimensional Radon and John transforms

DOI10.1016/j.jmaa.2021.125929zbMath1493.44005OpenAlexW4200384038MaRDI QIDQ2069770

Daniel Vera

Publication date: 21 January 2022

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2021.125929

zbMATH Keywords

Radon transforminverse problemsX-ray transformshearletsJohn transform

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Radon transform (44A12) Numerical methods for inverse problems for integral equations (65R32)

Uses Software

• ShearLab

Cites Work

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• Optimal recovery of 3D X-ray tomographic data via shearlet decomposition
• Shearlets. Multiscale analysis for multivariate data.
• 3D discrete X-ray transform
• Radon transform inversion using the shearlet representation
• The X-ray transform
• 3D Fourier based discrete Radon transform.
• Recovering edges in ill-posed inverse problems: Optimality of curvelet frames.
• Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
• The Radon transform intertwines wavelets and shearlets
• Wavelets with composite dilations and their MRA properties
• Optimally Sparse Representations of 3D Data with $C^2$ Surface Singularities Using Parseval Frames of Shearlets
• ShearLab: A Rational Design of a Digital Parabolic Scaling Algorithm
• Optimally Sparse Multidimensional Representation Using Shearlets
• The Radon Transform and Medical Imaging

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