Time-Dependent Problems in Imaging and Parameter Identification
暫譯: 影像與參數識別中的時間依賴性問題

Kaltenbacher, Barbara, Schuster, Thomas, Wald, Anne

Time-Dependent Problems in Imaging and Parameter Identification
  • 出版商: Springer
  • 出版日期: 2021-02-24
  • 售價: $6,780
  • 貴賓價: 9.5 折 $6,441
  • 語言: 英文
  • 頁數: 456
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 303057783X
  • ISBN-13: 9783030577834

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相關主題

商品描述

Inverse problems such as imaging or parameter identification deal with the recovery of unknown quantities from indirect observations, connected via a model describing the underlying context. While traditionally inverse problems are formulated and investigated in a static setting, we observe a significant increase of interest in time-dependence in a growing number of important applications over the last few years. Here, time-dependence affects a) the unknown function to be recovered and / or b) the observed data and / or c) the underlying process. Challenging applications in the field of imaging and parameter identification are techniques such as photoacoustic tomography, elastography, dynamic computerized or emission tomography, dynamic magnetic resonance imaging, super-resolution in image sequences and videos, health monitoring of elastic structures, optical flow problems or magnetic particle imaging to name only a few. Such problems demand for innovation concerning their mathematical description and analysis as well as computational approaches for their solution.

商品描述(中文翻譯)

逆問題，例如成像或參數識別，涉及從間接觀測中恢復未知量，這些觀測通過描述基礎背景的模型相連。雖然傳統上逆問題是在靜態環境中進行公式化和研究，但我們觀察到在過去幾年中，對時間依賴性的興趣顯著增加，並且在越來越多的重要應用中變得越來越重要。在這裡，時間依賴性影響 a) 要恢復的未知函數和/或 b) 觀測數據和/或 c) 基礎過程。在成像和參數識別領域中，具有挑戰性的應用包括光聲斷層成像、彈性成像、動態計算機斷層掃描或發射斷層掃描、動態磁共振成像、圖像序列和視頻中的超解析度、彈性結構的健康監測、光流問題或磁性粒子成像等。這些問題對其數學描述和分析以及解決方案的計算方法提出了創新需求。

作者簡介

Barbara Kaltenbacher has received her PhD (1996) and her Habilitation (2003) in mathematics at the University of Linz. After professor positions for optimization at the University of Stuttgart and for applied mathematics at the University of Graz, she is professor of Applied Analysis at the University of Klagenfurt since 2011. Her reseach interests lie in the field of inverse problems, in particular regularization methods and parameter identification in partial differential equations, as well as in modeling, for example in nonlinear acoustics and piezoelectricity. She has co-authored tree research monographs and published more than 100 refereed journal and proceedings papers. This work has been supported by the Austrian and the German Science Foundations, as well as by industrial partners in a number of projects. She currently serves as an editorial board member for Inverse Problems and the IMA Journal of Numerical Analysis as well as an editor in chief of the Journal of the European Mathematical Society.
Thomas Schuster studied mathematics and computer science at Saarland University in Saarbrücken where he also got his PhD (1999) and Habilitation (2004). After positions as a Visiting Assistant Professor at Tufts University Medford, MA, USA, as an Associate Professor for Applied Mathematics at Helmut Schmidt University Hamburg, as a Full Professor for Numerical Mathematics in Oldenburg he holds since 2012 a Chair as Full Professor for Numerical Mathematics at Saarland University in Saarbrücken. His research are theoretical foundations and applications for inverse and ill-posed problems. Besides the extension of regularization theory from classical settings to Banach spaces, he currently investigates the application of concepts from machine learning to the solution of inverse problems. The applications of his research range from computerized and terahertz tomography, vector and tensor field tomography, to magnetic particle imaging and damage detection in elastic materials. He co-authored three monographs and published more than 60 journal and proceeding articles. His research was supported by the German Science Foundation, the Federal Ministry of Education and Research, the Federal Ministry for Economic Affairs and Energy, and industrial partners. Currently he acts as an Editorial Board Member of Inverse Problems and Mathematical Problems in Engineering.
Anne Wald studied mathematics and physics at Saarland University in Saarbrücken, Germany. She received her master's degree in mathematics in 2012 and her diploma in physics in 2013. In 2017, she finished her Ph.D., also at Saarland University, where she currently works as a senior researcher. In her research, she mainly focuses on inverse problems in medicine and engineering, particularly on modeling aspects, mathematical analysis as well as fast and stable solution techniques. Applications include terahertz tomography, magnetic particle imaging, computerized tomography, and parameter identification for the monitoring of material structure. Her research is partly funded by the German Ministry of Education and Research.

作者簡介(中文翻譯)

巴巴拉·卡爾滕巴赫（Barbara Kaltenbacher）於1996年在林茲大學獲得數學博士學位（PhD），並於2003年獲得資格認證（Habilitation）。在斯圖加特大學擔任優化教授及在格拉茨大學擔任應用數學教授後，自2011年起，她成為克拉根福大學的應用分析教授。她的研究興趣集中在反問題領域，特別是正則化方法和偏微分方程中的參數識別，以及建模，例如在非線性聲學和壓電學方面。她共同撰寫了三本研究專著，並發表了超過100篇經過審核的期刊和會議論文。這些工作得到了奧地利和德國科學基金會的支持，以及多個項目的工業合作夥伴的支持。她目前擔任《反問題》（Inverse Problems）和《IMA數值分析期刊》（IMA Journal of Numerical Analysis）的編輯委員會成員，以及《歐洲數學學會期刊》（Journal of the European Mathematical Society）的主編。

托馬斯·舒斯特（Thomas Schuster）在德國薩爾布呂肯的薩爾蘭大學學習數學和計算機科學，並於1999年獲得博士學位（PhD）和2004年獲得資格認證（Habilitation）。在美國麻薩諸塞州梅德福的塔夫茨大學擔任訪問助理教授後，他在漢堡的赫爾穆特·施密特大學擔任應用數學副教授，並在奧爾登堡擔任數值數學全職教授，自2012年起在薩爾蘭大學擔任數值數學全職教授。他的研究集中在反問題和病態問題的理論基礎及應用上。除了將正則化理論從經典設置擴展到巴拿赫空間外，他目前還研究機器學習概念在解決反問題中的應用。他的研究應用範圍包括計算機化和太赫茲斷層掃描、向量和張量場斷層掃描、磁性粒子成像以及彈性材料中的損傷檢測。他共同撰寫了三本專著，並發表了超過60篇期刊和會議文章。他的研究得到了德國科學基金會、聯邦教育和研究部、聯邦經濟事務和能源部以及工業合作夥伴的支持。目前，他擔任《反問題》（Inverse Problems）和《工程中的數學問題》（Mathematical Problems in Engineering）的編輯委員會成員。

安妮·瓦爾德（Anne Wald）在德國薩爾布呂肯的薩爾蘭大學學習數學和物理。她於2012年獲得數學碩士學位，並於2013年獲得物理文憑。2017年，她在薩爾蘭大學完成博士學位（Ph.D.），目前擔任高級研究員。她的研究主要集中在醫學和工程中的反問題，特別是在建模方面、數學分析以及快速穩定的解決技術。應用包括太赫茲斷層掃描、磁性粒子成像、計算機斷層掃描以及材料結構監測的參數識別。她的研究部分由德國教育和研究部資助。

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