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@INPROCEEDINGS{Baumeister:941239,
      author       = {Baumeister, Paul F. and Bangun, Arya and Weber, Dieter},
      title        = {{A} {C}ircular {H}armonic {O}scillator {B}asis},
      reportid     = {FZJ-2023-00834},
      year         = {2022},
      abstract     = {Polar coordinates are frequently used to transform 2D
                      images appearing in 4D scanning transmission electron
                      microscopy (4D-STEM) as the dominant feature of the
                      ronchigram is a central spot where the undeflected electron
                      beam hits the detector. The information of interest resides
                      in the deviations from a circular shape of the spot. The
                      function basis of the quantum mechanical harmonic
                      osciallator consists of Hermite polynomials and a Gaussian
                      envelope function for the one-dimensional problem. For the
                      two-dimensional isotropic problem, the basis can be
                      represented either as a Cartesian product of two 1D basis
                      functions or in polar coordinates.A unitary transformation
                      connects both representations. To allow fast and affordable
                      compression of STEM images, we incorporate the Cartesian
                      product representation as it leads to two successive
                      matrix-matrix multiplications. This compression method is
                      particularly suitable for single-side-band (SSB)
                      ptychography. We present the explicit shape of the
                      associated radial functions of a circular harmonic
                      oscillator and compression factors in relation to
                      computational costs for a typical SSB ptychography
                      application.},
      month         = {Jun},
      date          = {2022-06-27},
      organization  = {Platform for Advanced Scientific
                       Computing Conference 2022, Basel
                       (Switzerland), 27 Jun 2022 - 29 Jun
                       2022},
      subtyp        = {After Call},
      cin          = {JSC / ER-C-1 / ER-C},
      cid          = {I:(DE-Juel1)JSC-20090406 / I:(DE-Juel1)ER-C-1-20170209 /
                      I:(DE-Juel1)ER-C-20211020},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5111},
      typ          = {PUB:(DE-HGF)24},
      url          = {https://juser.fz-juelich.de/record/941239},
}