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摘要
In this paper we investigate convergence properties of Tikhonov regularization for linear ill-posed problems under a stochastic error model. Namely, we assume that we are given a finite amount of measurements, each contaminated by Gaussian noise with zero mean and known finite variance. Using Besov-space penalty terms to promote sparse solutions with respect to a preassigned wavelet basis, the Ky Fan metric allows us to lift deterministic convergence results into the stochastic setting. In particular, we formulate a general convergence theorem and propose a formula to directly calculate a suitable regularization parameter. This immediately leads to convergence rates. Numerical examples are presented to verify the theoretical results.
- 出版日期2014-5
