Abel inversion using total variation regularization: applications

DOI10.1080/17415970600882549zbMath1200.65115OpenAlexW2025246384MaRDI QIDQ3059473

Brendt Wohlberg, Kevin R. Vixie, Collin Powell, Patrick R. Campbell, Thomas J. Asaki, Rick Chartrand

Publication date: 25 November 2010

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415970600882549

zbMATH Keywords

total variationregularizationinverse problemstomographyAbel transform

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Numerical methods based on nonlinear programming (49M37) Biomedical imaging and signal processing (92C55) Inverse problems in linear algebra (15A29) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Numerical methods for inverse problems for integral equations (65R32) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Inverse problems for integral equations (45Q05)

Related Items (10)

A blocking scheme for dimension-robust Gibbs sampling in large-scale image deblurring ⋮ Hybrid regularized cone-beam reconstruction for axially symmetric object tomography ⋮ Quantitative Abel tomography robust to noisy, corrupted and missing data ⋮ Stability and error estimates of BV solutions to the Abel inverse problem ⋮ Numerical differentiation of noisy, nonsmooth data ⋮ A fast algorithm for the inversion of Abel's transform ⋮ Uncertainty Quantification of Density Reconstruction Using MCMC Method in High-Energy X-ray Radiography ⋮ High-order total variation regularization approach for axially symmetric object tomography from a single radiograph ⋮ An efficient solution of system of generalized Abel integral equations using Bernstein polynomials wavelet bases ⋮ Bayesian Abel Inversion in Quantitative X-Ray Radiography

Cites Work

• Abel inversion using total-variation regularization
• On the Convergence of the Lagged Diffusivity Fixed Point Method in Total Variation Image Restoration
• Computational Methods for Inverse Problems

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