Tikhonov Regularization Using Sobolev Metrics
نویسندگان
چکیده
Given an ill-posed linear operator equation Au = f in a Hilbert space, we formulate a variational problem using Tikhonov regularization with a Sobolev norm of u, and we treat the variational problem by a Sobolev gradient flow. We show that the gradient system has a unique global solution for which the asymptotic limit exists with convergence in the strong sense using the Sobolev norm, and that the variational problem therefore has a unique global solution. We present results of numerical experiments that demonstrates the benefits of using a Sobolev norm for the regularizing term.
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