Iterative Methods for Approximate Solution of Inverse Problems

By A. Bakushinsky, M. Kokurin. 2005

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Real‐time MRI at a resolution of 20 ms (2010, methodology): “As a consequence, the MRI signal equation becomes a nonlinear equation, which may be solved with numerical methods, such as the iteratively regularized Gauss–Newton method (22).”
Approximate source conditions in Tikhonov–Phillips regularization and consequences for inverse problems with multiplication operators (2006, background): “Properties concerning the fact that source conditions are valid quite general in such approximate manner were also studied in a more general context in the recent book [4].”
KACZMARZ METHODS FOR REGULARIZING NONLINEAR ILL-POSED EQUATIONS I: CONVERGENCE ANALYSIS (2007, methodology): “, [15, 10, 6, 1, 12]) and Tikhonov type regularization methods [25, 24, 23, 19, 6].”
Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems (2009, background): “So far, to the authors best knowledge, iterative solvers for nonlinear ill-posed problems in Banach spaces have only been formulated in [4] (see section 4.”