Research and projects

The Research Group Regularization is in close cooperation with other groups working on inverse problems.

Research focus

• Oversmoothing regularization models in the light of local incorrectness phenomena
• Source representations for describing smoothness (SCIP)
• Regularization of ill-posed problems in laser optics
• The nature of incorrectness and adapted regularization approaches
• Inverse and incorrect problems from natural sciences, economics, technology and finance

Current results of this research work at:
     Research results (Download fulltext article)

DFG -- Research project HO 1454/13-1 -- Project-id: 453804957 (2021-2025)

• Oversmoothing regularization models in light of local ill-posedness phenomena
  (Current DFG-financed employee: Dr. Yu Deng)
• Cooperation project with Prof. Dr. Robert Plato (University Siegen)

Co-Responsibility for DFG -- Research Project-id: 513566305 (2023-2025)

• Advances in regularization theory for inverse problems in Banach spaces
  PI: Prof. Irwin Yousept (Univ. Duisburg-Essen)

Completed DFG -- Research project HO 1454/12-1 -- Projektnummer: 391100538 (2018-2022)

• Novel Error Measures and Source Conditions of Regularization Methods for Inverse Problems (SCIP)
• Cooperation project within the framework of a German-Austrian research project of the D-A-CH lead agency agreement with the Institute for Mathematics at the University of Vienna (Prof. Dr. Otmar Scherzer)
  DFG-funded project associate: M.Sc. Christopher Hofmann, PhD obtained 2020

Completed DFG -- Research project HO 1454/10-1 (2016-2019)

• Regularization strategies for advanced laser pulse shape reconstruction
• Cooperation project with the Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy Berlin
  (Prof. Dr. Günter Steinmeyer)
  DFG-funded project associate: Dr. Daniel Gerth

Completed DFG -- Research project HO 1454/8-2 (2016)

• Regularization of nonlinear ill-posed problems in Banach spaces and conditional stability.
  DFG-funded project associate: Dr. Daniel Gerth

Completed DFG -- Research project FL 832/1-2 (2015-2016)

• Regularization of autoconvolution and other ill-posed equations of quadratic structure with applications in laser optics.
• The follow-up project to complete the topic.
• DFG-funded project associate: Dipl.-Math. Steven Bürger

Completed DFG -- Research project FL 832/1-1 und HO 1454/9-1 (2013-2015)

• Regularization of autoconvolution and other ill-posed equations of quadratic structure with applications in laser optics
• DFG-funded project associate: Dipl.-Math. Steven Bürger, Dr. Stephan Anzengruber (bis 3/2015) and Dr. Daniel Gerth (ab 10/2015). Cooperation project with the Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy Berlin (PD Dr. Günter Steinmeyer)

Completed DFG -- Research project HO 1454/8-1 (2011-2014)

• Regularization of nonlinear ill-posed problems in Banach spaces and conditional stability: Cooperation project with Fudan University Shanghai (Prof. Jin Cheng) as part of the trilateral initiative "Inverse Problems" China-Finland-Germany

Completed DFG-Research project HO 1454/7-2 (2008-2011)

• Nature of the incorrectness, approximate source representations and adapted regularization methods in identification problems:
  Project P2 of the DFG project package: "Numerische Simulation gekoppelter Aufgaben der Mechanik"