Mini-Workshop - Image Reconstruction and Learning

September 09-11, 2015 - Innsbruck

From a general perspective, an image can be seen as a distribution of a physical quantity in some area or volume. Such a quantity could represent pressure, absorption coefficient, concentration of tracer molecules, or potential of gravitational and magnetic fields. Often, these images are either not directly accessible, or their direct access is expensive. In mathematical image reconstruction one tries to recover the image from accessible indirect measurement data. Image reconstruction can be seen as a mathematical inverse problem, and arises, for instance, in various tomographic imaging methods. Examples include x-ray computed tomography, emission tomographies (PET, SPECT), magnetic resonance imaging, photoacoustic imaging, fluorescence microscopy, recovery of geopotentials from satellite data, or compressed sensing. One of the aims of this workshop is to present and discuss recent developments of mathematical image reconstruction in various scientific fields.

Often the image reconstruction process depends on various parameters whose values are a priori unknown. These parameters may depend on the measurement data or on the specific setup of the data collection process. An explicit expression describing such a dependence is, however, usually unknown. Statistical learning techniques are designed for estimating the functional dependence between various parameters using statistical observations of parameters' values. It seems promising to use the statistical learning approach for estimating unknown parameters in image reconstruction. Therefore, another aim of the workshop is the consideration of current trends in the field of statistical learning. The workshop represents a forum for the exchange of the scientific ideas between experts in image reconstruction and experts in statistical learning.

In this workshop, leading experts will report on recent progress towards using deep learning for various imaging applications.

List of confirmed speakers

• Jürgen Frikel (Technical University of Denmark)
  Joint reconstruction and segmentation using the Potts model

• Christian Gerhards (University of Vienna)
  Some recent problems in Geomathematics

• Jan Keller-Findeisen (Max Planck Institute for Biophysical Chemistry, Göttingen)
  From micro to nano – A history of super-resolution fluorescence microscopy

• Richard Kowar (University of Innsbruck)
  On time reversal in photoacoustic tomography for tissue similar to water

• Andreas Maurer (Munich)
  Estimating the reconstruction error for a class of coding schemes

• Sergiy Pereverzyev Jr. (University of Innsbruck)
  On some novel applications of statistical classification

• Simon Rabanser (University of Innsbruck)
  Single-stage reconstruction for quantitative photoacoustic tomography

• Alessandro Rudi (Istituto Italiano di Tecnologia, Genoa)
  Less is more: Nyström for large scale learning

• Saverio Salzo (University of Genoa)
  Consistent learning by composite proximal thresholding.

• Haisen Ta (Max Planck Institute for Biophysical Chemistry, Göttingen)
  Mapping molecules in scanning far-field fluorescence nanoscopy

• Pavlo Tkachenko (Radon Institute for Computational and Applied Mathematics, Linz)
  A linear functional strategy as an alternative to a parameter choice for learning problems

• Christoph Wolf (University of Innsbruck)
  Compressive time-of-flight 3D imaging

Schedule