Combining image reconstruction and image evaluation

• Applicant: Professor Dr. Alfred Karl Louis
• Subject Area: Mathematics
• Term: from 2009 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 129883162

• Final Report Year: 2017

Final Report Abstract

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.

Publications

• 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.
  (See online at 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.
  (See online at 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.
  (See online at 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.
  (See online at 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.
  (See online at 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.