Abstract
SUMMARY We analyze the energy method for inverse problems. We study the unconstrained minimization of the energy functional consisting of a least-square fidelity term and tw o other regularization terms being the seminorm in the BV space and the norm in the G space. We consider a coercive (non)linear operator modelling the forward problem. We establish the uniqueness and stability results for the minimization problems. The stability is studied with respect to the perturbations in th e data, in the operator, as well as in the regularization parameters. We settle convergence results for the general minimization schemes. Copyright c 2009 John Wiley & Sons, Ltd.
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