Analysis of the bounded variation and the G regularization for nonlinear inverse problems

作者：Cimrak I^*

来源：Mathematical Methods in the Applied Sciences, 2010, 33(9): 1102-1111.

DOI：10.1002/mma.1239

• image decomposition
• Banach spaces
• bounded variation
• total variation
• G norm
• regularization

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 two 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 the data, in the operator, as well as in the regularization parameters. We settle convergence results for the general minimization schemes.

• 出版日期2010-6