DSpace Arşivi :: by Yazar "Rastogi, Abhishake" değerine göre listeleniyor

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Regularization schemes for statistical inverse problems
(Maltepe Üniversitesi, 2019) Rastogi, Abhishake
We study a statistical inverse learning problem, where we observe the noisy image of a quantity through a operator at some random design points. We consider the regularization schemes to reconstruct the estimator of the quantity for the ill-posed inverse problem. We develop a theoretical analysis for the minimizer of the regularization scheme using the ansatz of reproducing kernel Hilbert spaces. We discuss optimal rates of convergence for the proposed scheme, uniformly over classes of admissible solutions, defined through appropriate source conditions.
Tikhonov regularization with oversmoothing penalty for linear statistical inverse learning problems
(Maltepe Üniversitesi, 2019) Rastogi, Abhishake
In this paper, we consider the linear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered in the reproducing kernel Hilbert space framework to reconstruct the estimator from the random noisy data. We discuss the rates of convergence for the regularized solution under the prior assumptions and link condition. For regression functions with smoothness given in terms of source conditions the error bound can explicitly be established.