An improved preconditioned LSQR for discrete ill-posed problems
Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
EURASIP Journal on Applied Signal Processing
The Lagrange method for the regularization of discrete ill-posed problems
Computational Optimization and Applications - Special issue: Numerical analysis of optimization in partial differential equations
Greedy Tikhonov regularization for large linear ill-posed problems
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
The Lagrange method for the regularization of discrete ill-posed problems
Computational Optimization and Applications
Large-Scale Image Deblurring in Java
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
Robust constrained receding-horizon predictive control via bounded data uncertainties
Mathematics and Computers in Simulation
Arnoldi-Tikhonov regularization methods
Journal of Computational and Applied Mathematics
Superresolution reconstruction using nonlinear gradient-based regularization
Multidimensional Systems and Signal Processing
Computers & Mathematics with Applications
FIMH'07 Proceedings of the 4th international conference on Functional imaging and modeling of the heart
UPRE method for total variation parameter selection
Signal Processing
Some aspects of band-limited extrapolations
IEEE Transactions on Signal Processing
Computational Statistics & Data Analysis
An iterative Lagrange method for the regularization of discrete ill-posed inverse problems
Computers & Mathematics with Applications
Nonnegative matrix factorization with bounded total variational regularization for face recognition
Pattern Recognition Letters
Pattern Recognition Letters
The ill-posedness of the sampling problem and regularized sampling algorithm
Digital Signal Processing
An Efficient Iterative Approach for Large-Scale Separable Nonlinear Inverse Problems
SIAM Journal on Scientific Computing
Original Article: Comparingparameter choice methods for regularization of ill-posed problems
Mathematics and Computers in Simulation
A Regularized Gauss-Newton Trust Region Approach to Imaging in Diffuse Optical Tomography
SIAM Journal on Scientific Computing
A regularised estimator for long-range dependent processes
Automatica (Journal of IFAC)
A Dynamical Tikhonov Regularization for Solving Ill-posed Linear Algebraic Systems
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Automatic parameter setting for Arnoldi-Tikhonov methods
Journal of Computational and Applied Mathematics
A control Liapunov function approach to generalized and regularized descent methods for zero finding
International Journal of Hybrid Intelligent Systems
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Numerical solution of ill-posed problems is often accomplished by discretization (projection onto a finite dimensional subspace) followed by regularization. If the discrete problem has high dimension, though, typically we compute an approximate solution by projecting the discrete problem onto an even smaller dimensional space, via iterative methods based on Krylov subspaces. In this work we present a common framework for efficient algorithms that regularize after this second projection rather than before it. We show that determining regularization parameters based on the final projected problem rather than on the original discretization has firmer justification and often involves less computational expense. We prove some results on the approximate equivalence of this approach to other forms of regularization, and we present numerical examples.