Kombination von Bildrekonstruktion und Bildauswertung

• Antragsteller: Professor Dr. Alfred Karl Louis
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2009 bis 2016
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 129883162

• Erstellungsjahr: 2017

Zusammenfassung der Projektergebnisse

We succeeded in presenting the combined reconstruction and image analysis as a valuable tool for reconstruction which allows for better evaluating the information content of reconstructions. In that way even classifications can be applied as a further tool. Both in classical X-ray tomography, now even for the modern cone beam tomography, as well as for other imaging modalities the approach results in very efficient algorithms with many possible and even already realized applications.

Projektbezogene Publikationen (Auswahl)

• Inverse Design of Anti-Reflection Coatings using the Nonlinear Approximate Inverse. Inverse Problems in Science and Engineering, 24(6), 917-935
  Abazid, M.A., Lakhal, A., Louis, A.K.
  
• Efficient algorithms for linear dynamic inverse problems with known motion. Inverse Problems 30 (2014) 035008
  Hahn, B.N.
  (Siehe online unter https://doi.org/10.1088/0266-5611/30/3/035008)
• Series Expansions of the Reconstruction Kernel of the Radon Transform over a Cormack-Type Family of Curves with Applications in Tomography. SIAM Journal on Imaging Sciences, 7(2), 924943, 2014
  Rigaud, G., Lakhal, A., Louis, A.K.
  (Siehe online unter https://doi.org/10.1137/130942784)
• Approximate inverse and Sobolev estimates for the attenuated Radon transform. Inverse Problems 31 (2015) 105010
  Rigaud, G., Lakhal, A.
  (Siehe online unter https://doi.org/10.1088/0266-5611/31/10/105010)
• Image and feature reconstruction for the attenuated Radon transform via circular harmonic decomposition of the kernel Inverse Problems 31 (2015) 025007
  Rigaud, G., Lakhal, A.
  (Siehe online unter https://doi.org/10.1088/0266-5611/31/2/025007)
• Exact cone beam reconstruction formulae for functions and their gradients for spherical and flat detectors. Inverse Problems 32 (2016) 115005
  Louis, A.K.
  (Siehe online unter https://doi.org/10.1088/0266-5611/32/11/115005)
• Reconstruction methods for severely ill-posed and nonlinear inverse problems applied on electromagnetics, medical imaging, finance; Habilitation thesis, Saarbrücken, 2016
  Lakhal, A.