Testable uniqueness conditions for empirical assessment of undersampling levels in total variation-regularized X-ray CT

DOI10.1080/17415977.2014.986724zbMath1326.94023arXiv1409.0214OpenAlexW2083738609MaRDI QIDQ3456555

Dirk A. Lorenz, Christian Kruschel, Jakob Sauer Jørgensen

Publication date: 9 December 2015

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

Full work available at URL: https://arxiv.org/abs/1409.0214

zbMATH Keywords

total variationcomputed tomographysparse regularizationuniqueness conditions

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Ill-posedness and regularization problems in numerical linear algebra (65F22) Computing methodologies for image processing (68U10) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Numerical methods for inverse problems for integral equations (65R32) Sampling theory in information and communication theory (94A20)

Related Items

Shearlet-based regularization in statistical inverse learning with an application to x-ray tomography ⋮ Image reconstruction using analysis model prior ⋮ Empirical average-case relation between undersampling and sparsity in X-ray CT

Uses Software

• Mosek
• AIR tools

Cites Work

• Nonlinear total variation based noise removal algorithms
• A mathematical introduction to compressive sensing
• The benefit of group sparsity
• The cosparse analysis model and algorithms
• A first-order primal-dual algorithm for convex problems with applications to imaging
• AIR tools -- a MATLAB package of algebraic iterative reconstruction methods
• Average case recovery analysis of tomographic compressive sensing
• Linear convergence rates for Tikhonov regularization with positively homogeneous functionals
• A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science
• Necessary and sufficient conditions for linear convergence of ℓ1-regularization
• Compressed Sensing: How Sharp Is the Restricted Isometry Property?
• Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
• On Polar Polytopes and the Recovery of Sparse Representations
• Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing
• Sparse and Redundant Representations
• Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities
• Atomic Decomposition by Basis Pursuit
• Stable Signal Reconstruction via $\ell^1$-Minimization in Redundant, Non-Tight Frames
• Near-Optimal Compressed Sensing Guarantees for Total Variation Minimization
• Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems
• Compressed sensing