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AN EFFICIENT ITERATIVE APPROACH FOR LARGE-SCALE SEPARABLE NONLINEAR INVERSE PROBLEMS
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AI
DOI：10.1137/080732213.png)
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Abstract
En 中文
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.
Keywords:
Gauss-Newton method
ill-posed inverse problems
iterative methods
Golub-Kahan bidiagonalization
hybrid method
Tikhonov regularization
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