Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization:New Results in Modern Theory of Inverse Problems and an Application in Laser Optics（Frontiers in Mathematics）
变分源条件、二次逆问题、稀疏性促进正则化：现代反问题理论的新结果与激光光学的应用
数理逻辑与数学基础售 价：
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800.00
发货周期：外国库房发货，通常付款后3-5周到货
出 版 社
出版时间
2018年09月18日
装 帧
平装
页 码
182
语 种
英文
版 次
1
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图书简介
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.
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