A descent method for regularization of ill-posed problems

DOI10.1080/10556780500140409zbMath1086.65054OpenAlexW1969434830MaRDI QIDQ5717546

Fabiana Zama, Elena Loli Piccolomini

Publication date: 10 January 2006

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556780500140409

zbMATH Keywords

inverse problemHilbert spacesTikhonov regularizationconjugate gradient iterationslinear compact operatorDescent methods

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (5)

Representation of high resolution images from low sampled Fourier data: applications to dynamic MRI ⋮ An experiment of parallel SPECT data reconstruction ⋮ Krylov methods for inverse problems: Surveying classical, and introducing new, algorithmic approaches ⋮ An inner-outer regularizing method for ill-posed problems ⋮ An automatic regularization parameter selection algorithm in the total variation model for image deblurring

Uses Software

• Regularization tools

Cites Work

• Unnamed Item
• The discrete Picard condition for discrete ill-posed problems
• Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
• A B-spline parametric model for high resolution dynamic magnetic resonance imaging
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• A Trust-Region Approach to the Regularization of Large-Scale Discrete Forms of Ill-Posed Problems
• The Conjugate Gradient Method and Trust Regions in Large Scale Optimization
• Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy
• Fast CG-Based Methods for Tikhonov--Phillips Regularization
• The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems
• Test Matrices for Regularization Methods

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