Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization (eBook, PDF)
Jens Flemming
eBook, PDF

Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization (eBook, PDF)

New Results in Modern Theory of Inverse Problems and an Application in Laser Optics

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The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined.Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate...

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