A Hybrid LSMR Algorithm for Large-Scale Tikhonov Regularization

DOI10.1137/140975024zbMath1325.65057OpenAlexW1847144746MaRDI QIDQ3449797

Julianne Chung, Katrina Palmer

Publication date: 30 October 2015

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/92d470f23262b4534bc37eb99b68541789f03f0a

zbMATH Keywords

iterative methodsTikhonov regularizationill-posed inverse problemshybrid regularization

Mathematics Subject Classification ID

Related Items (11)

Regularization properties of Krylov iterative solvers CGME and LSMR for linear discrete ill-posed problems with an application to truncated randomized SVDs ⋮ Noise representation in residuals of LSQR, LSMR, and CRAIG regularization ⋮ A relaxed iterated Tikhonov regularization for linear ill-posed inverse problems ⋮ Efficient generalized Golub–Kahan based methods for dynamic inverse problems ⋮ Generalized Hybrid Iterative Methods for Large-Scale Bayesian Inverse Problems ⋮ Hybrid Projection Methods with Recycling for Inverse Problems ⋮ The regularizing properties of global GMRES for solving large-scale linear discrete ill-posed problems with several right-hand sides ⋮ Approximation accuracy of the Krylov subspaces for linear discrete ill-posed problems ⋮ Flexible Krylov Methods for $\ell_p$ Regularization ⋮ Hybrid Projection Methods with Recycling for Inverse Problems ⋮ Hybrid projection methods for large-scale inverse problems with mixed Gaussian priors

Uses Software

• GKB-FP
• PROPACK
• LSMR
• CRAIG

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An augmented LSQR method
• A weighted-GCV method for Lanczos-hybrid regularization
• Noise propagation in regularizing iterations for image deblurring
• A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations
• The behavior of eigenvalues and singular values under perturbations of restricted rank
• Rank-one modification of the symmetric eigenproblem
• Regularization methods for large-scale problems
• An implicit shift bidiagonalization algorithm for ill-posed systems
• Tikhonov regularization of large linear problems
• Iterative methods for image deblurring: A Matlab object-oriented approach
• GKB-FP: An algorithm for large-scale discrete ill-posed problems
• Estimation of the \(L\)-curve via Lanczos bidiagonalization
• Two new efficient iterative regularization methods for image restoration problems
• Regularization parameter estimation for large-scale Tikhonov regularization using a priori information
• The regularizing effect of the Golub-Kahan iterative bidiagonalization and revealing the noise level in the data
• Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems
• An Efficient Iterative Approach for Large-Scale Separable Nonlinear Inverse Problems
• LSMR: An Iterative Algorithm for Sparse Least-Squares Problems
• Deblurring Images
• Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
• A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix
• A Bidiagonalization-Regularization Procedure for Large Scale Discretizations of Ill-Posed Problems
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Rank-Deficient and Discrete Ill-Posed Problems
• Linear and Nonlinear Inverse Problems with Practical Applications
• Tikhonov Regularization with a Solution Constraint
• Computational Methods for Inverse Problems
• De-noising by soft-thresholding
• Large-Scale Inverse Problems in Imaging
• Discrete Inverse Problems
• A Projection‐Based Approach to General‐Form Tikhonov Regularization
• Numerical methods for coupled super-resolution

This page was built for publication: A Hybrid LSMR Algorithm for Large-Scale Tikhonov Regularization