Measurements in nanoscopic imaging suffer from blurring effects concerning different point spread functions (PSF). Some apparatus even have PSFs that are locally dependent on phase shifts. Additionally, raw data are affected by Poisson noise resulting from laser sampling and ”photon counts” in fluorescence microscopy. In these applications standard reconstruction methods (EM, filtered backprojection) deliver unsatisfactory and noisy results. Starting from a statistical modeling in terms of a MAP likelihood estimation we combine the iterative EM algorithm with TV regularization techniques to make an efficient use of a-priori information. Typically, TV-based methods deliver reconstructed cartoon-images suffering from contrast reduction. We propose an extension to EM-TV, based on Bregman iterations and inverse scale space methods, in order to obtain improved imaging results by simultaneous contrast enhancement. We illustrate our techniques by synthetic and experimental biological data.

@InProceedings{BSB09a,
  author       = {Brune, C. and Sawatzky, A. and Burger, M.},
  title        = {Bregman-EM-TV Methods with Application to Optical Nanoscopy},
  booktitle    = {Proceedings of the 2nd International Conference on Scale Space and Variational Methods in Computer Vision},
  series       = {LNCS},
  volume       = {5567},
  pages        = {235--246},
  month        = {april},
  year         = {2009},
  editor       = {(Eds.) X.-C. Tai et al.},
  publisher    = {Springer},
  doi          = {10.1007/978-3-642-02256-2_20},
  url          = \{/2009/BSB09a},
}