Bregman-EM-TV Methods with Application to Optical Nanoscopy

  • Christoph Brune
  • Alex Sawatzky
  • Martin Burger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5567)

Abstract

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.

Keywords

Point Spread Function Poisson Noise Order Optimality Condition Total Variation Regularization Iterative Regularization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Christoph Brune
    • 1
  • Alex Sawatzky
    • 1
  • Martin Burger
    • 1
  1. 1.Institut für Numerische und Angewandte MathematikWestfälische Wilhelms-Universität MünsterMünsterGermany

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