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Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization = New Results in Modern Theory of Inverse Problems and an Application in Laser Optics /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization/ by Jens Flemming.
其他題名:	New Results in Modern Theory of Inverse Problems and an Application in Laser Optics /
作者:	Flemming, Jens.
面頁冊數:	XI, 182 p. 35 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Numerical analysis. -
電子資源:	https://doi.org/10.1007/978-3-319-95264-2
ISBN:	9783319952642

Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization = New Results in Modern Theory of Inverse Problems and an Application in Laser Optics /
Flemming, Jens.

Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting RegularizationNew Results in Modern Theory of Inverse Problems and an Application in Laser Optics /[electronic resource] :by Jens Flemming. - 1st ed. 2018. - XI, 182 p. 35 illus.online resource. - Frontiers in Mathematics,1660-8046. - Frontiers in Mathematics,.

Inverse problems, ill-posedness, regularization -- Variational source conditions yield convergence rates -- Existence of variational source conditions -- What are quadratic inverse problems? -- Tikhonov regularization -- Regularization by decomposition -- Variational source conditions -- Aren’t all questions answered? -- Sparsity and 1-regularization -- Ill-posedness in the l1-setting -- Convergence rates.

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 results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics. Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.

ISBN: 9783319952642

Standard No.: 10.1007/978-3-319-95264-2doiSubjects--Topical Terms:

527939
Numerical analysis.

LC Class. No.: QA297-299.4

Dewey Class. No.: 518

Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization = New Results in Modern Theory of Inverse Problems and an Application in Laser Optics /
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