Dr. Erdem Altuntac

• Orthogonal representation bases, i.e. wavelets, DCT, DFT
  
• Image based dictionaries
  

• Conventional quadratic-Tikhonov regularization
  
• Gradient-based algorithms
  
• Primal-dual splitting
  
• Proximal mapping
  
• Rules for the choice of the regularization parameter
  
• Convergence analysis (with the assumption of Variational Source Condition).
  

Applications;

• Depth completion from LiDAR based point-cloud data
  
• Image inpainting
  
• Computational image recovery
  
• Multidimensional tomographic image reconstruction; e.g. 3D atmospheric tomography
  
• Situational awareness by acoustics
  
• Parameter estimation in non-linear acoustics
  

Publications

• Cwalina, S., Kottke, C., Jungnickel, V., Freund, R., Runge, P., Rustige, P., Knieling, T., Gu-Stoppel, S., Albers, J., Laske, N., Senger, F., Wen, L., Giovanneschi, F., Altuntac, E., Rames, A. N., Huici, M. A. G., Küter, A., Reddy, S. Fiber-based frequency modulated LiDAR with MEMS scanning capability for long-range sensing inautomative applications. (to be presented at IEEE MetroAutomotive Workshop 2021) .


• Altuntac, E. Choice of the Parameters in A Primal-Dual Algorithm for Bregman Iterated Variational Regularization.
  https://doi.org/10.1007/s11075-020-00909-6 Numer Algor 86, 729–759 (2021).


• New Pair of Primal Dual Algorithms for Bregman Iterated Variational Regularization.
  https://arxiv.org/abs/1903.07392 March 2019.


• Altuntac, E. Variational Regularization Strategy for Atmospheric Tomography
  http://hdl.handle.net/11858/00-1735-0000-0028-87D4-7.
  Institute for Numerical and Applied Mathematics, University of Goettingen, July 2016.


• Altuntac, E. Generalized Variational Source Condition Associated with the Bregman Distance-I: Verification of the Variational Source Condition and Stability of the Total Error Estimation.
  https://arxiv.org/abs/1606.03650 . July 2016.


• Altuntac, E. Quasi-Newton Approach for an Atmospheric Tomography Problem.
  https://arxiv.org/abs/1511.08022 April 2016.


• Altuntac E. On convergence of an alternating method for a Cauchy problem for the Helmholtz equation.
  https://www.impan.pl/wydawnictwa/preprints_impan/p730.pdf IMPAN preprint 730, June 2011.

Numerical Instruments

During my doctoral studies, I have developed a special interest in coding up and implementation of some numerical tools that have been beneficial to my research. Addition to the list below, I have also performed some test implementations for the software SAMSARA developed by D. R. Luke.

• Primal-dual splitting for Bregman iterated variational regularization , March 2019.
• A Prototype for 3-D Atmospheric Tomography - II , March 2019.
• 3-D Smooth TV Functional and Its Gradient , August 2015.
• A Prototype for 3-D Atmospheric Tomography , August 2015.
• Basic 2-D Reconstruction Instruments , May 2014.

Conferences/Workshops/Summer Schools