| 书目名称 | Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization | | 副标题 | New Results in Moder | | 编辑 | Jens Flemming | | 视频video | | | 概述 | Presents recent research results in a consistent notation.Contributes to two very active fields of research.Shows that variational source condition always yields convergence rate results | | 丛书名称 | Frontiers in Mathematics | | 图书封面 |  | | 描述 | 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.. | | 出版日期 | Book 2018 | | 关键词 | inverse problem; ill-posedness; variational source condition; quadratic inverse problem; autoconvolution | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-95264-2 | | isbn_softcover | 978-3-319-95263-5 | | isbn_ebook | 978-3-319-95264-2Series ISSN 1660-8046 Series E-ISSN 1660-8054 | | issn_series | 1660-8046 | | copyright | Springer Nature Switzerland AG 2018 |
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发表于 2025-3-21 19:12:44
