Convergence Rates for Variational Regularization of Inverse Problems in Exponential Families PDF Download

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Convergence Rates for Variational Regularization of Inverse Problems in Exponential Families

Convergence Rates for Variational Regularization of Inverse Problems in Exponential Families PDF Author: Yusufu Simayi
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Languages : en
Pages : 0

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Book Description
We consider statistical inverse problems with statistical noise. By using regularization methods one can approximate the true solution of the inverse problem by a regularized solution. The previous investigation of convergence rates for variational regularization with Poisson and empirical process data is shown to be suboptimal. In this thesis we obtain improved convergence rates for variational regularization methods of nonlinear ill-posed inverse problems with certain stochastic noise models described by exponential families and derive better reconstruction error bounds by applying deviat...