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

• Main Author: Flemming, Jens (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Series: Frontiers in Mathematics,
• Subjects: Numerical analysis.; Operator theory.; Numerical Analysis.; Operator Theory.

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 litera...

Table of Contents:

• 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.