Institute for Mathematical Stochastics

BMBF INVERS - 03MUPAH6 - Health and Medical Technology:
Deconvolution with sparsity constraints in optical nanoscopy and mass spectroscopy


Project Managment:

  • Prof. Dr. Thorsten Hohage
  • Prof. Dr. Axel Munk


  • Dr. Thomas Hotz
  • Philipp Marnitz



Mass spectroscopy and light microscopy have been revolutionised over the last couple of years, changing the requirements of the accompanying data analytical methods. We hence aim at developing new approaches to analyse such data, making them available to our industry partners.


  • Deconvolution with a-priori known sparsity (T. Hohage, A. Munk, T. Hotz):
    Nowadays, light microscopy achieves resolutions which almost allow to localise individual fluorescing molecules. Thus, the common assumption used when
    applying reconstruction methods, namely that the object is (piecewise) smooth, is no longer fulfilled. Rather, the object compises few, bright and isolated points whose location and brightness are to reconstruct. This is to say they are extremely sparse, requiring penalties adapted to this situation: we are looking for reconstructions consisting of as few points as possible, while adequately explaining the data.
  • Local choice of penalties for image reconstruction in fluorescence microscopy (A. Munk, N. Bissantz, P. Marnitz):
    Reconstruction methods typically depend on some regularisation parameter allowing to balance data fit and roughness of the reconstruction. As the image structure as well as the underlying object's structure vary through the image, it is desirable to choose the regularisation parameter locally in an adaptive manner. Since statistical multiscale analysis has been proven well-suited to choose such a parameter globally for positron emission tomography (Bissantz, Mair, Munk: 2006), we envision to use it also for the problem of choosing the parameter locally.

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