Mathematics in Imaging

1. Foundations in electromagnetics and imaging
  • Propagation of waves
  • Scattering (e.g. surface scattering, volumetric scattering)
  • Phase, statistical optics, coherence optics
  • Image formation (e.g. tomography, telescope, microscopy, remote sensing, 
    multi-aperture system)
  • Theory and algorithms of optical element designs (e.g. computer generated hologram,
    volume holograms, photonic elements)
  • Nonlinear optics
  • Linear and nonlinear spectroscopy
 ​​2. Foundations in mathematics and signal processing
  • Variational or Bayesian regularization of inverse problems (e.g. total variation or frame
    based regularization)
  • Bilinear inverse problems (e.g. blind deblurring, self-calibration)
  • Sampling theory (e.g. compressive imaging, adaptive sampling)
  • Theory and algorithms of learning techniques (e.g. dictionary learning, neural networks)
  • Optimization theory and algorithms for convex and nonconvex problems (e.g. phase
    retrieval, inversion of multiple scattering)