A discrete L-curve for the regularization of ill-posed inverse problems
Abstract: In many applications, the discretization of continuous ill-posed inverse problems results in discrete ill-posed problems whose solution requires the use of regularization strategies. The L-curve criterium is a popular tool for choosing good regularized solutions, when the data noise norm is not a priori known. In this work, we propose replacing the original ill-posed inverse problem with a noise-independent equality constrained one and solving the corresponding first-order equations by the Newton method. The sequence of the computed iterates defines a new discrete L-curve. By numerical results, we show that good regularized solutions correspond with the corner of this L-curve.
Keywords: Newton method; L-curve; ill-posed inverse problems; regularization; constrained optimization.
Category 1: Applications -- Science and Engineering
Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )
Entry Submitted: 05/23/2012
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