SIAM Journal on Numerical Analysis
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
ACM Transactions on Mathematical Software (TOMS)
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems
ACM Transactions on Mathematical Software (TOMS)
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
A Trust-Region Approach to the Regularization of Large-Scale Discrete Forms of Ill-Posed Problems
SIAM Journal on Scientific Computing
Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems
SIAM Journal on Matrix Analysis and Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms)
A Projection-Based Approach to General-Form Tikhonov Regularization
SIAM Journal on Scientific Computing
Information Sciences: an International Journal
An efficient computational approach for multiframe blind deconvolution
Journal of Computational and Applied Mathematics
Constrained numerical optimization methods for blind deconvolution
Numerical Algorithms
Hi-index | 0.01 |
We present an efficient iterative approach to solving separable nonlinear least squares problems that arise in large-scale inverse problems. A variable projection Gauss-Newton method is used to solve the nonlinear least squares problem, and Tikhonov regularization is incorporated using an iterative hybrid scheme. Regularization parameters are chosen automatically using a weighted generalized cross validation method, thus providing a nonlinear solver that requires very little input from the user. Applications from image deblurring and digital tomosynthesis illustrate the effectiveness of the resulting numerical scheme.