MS 12: Numerical microlocal analysis

Thu, 30 March, 2017, 16:30–18:30, Room: UC 202DH


Marta Betcke and Jürgen Frikel


One of the defining properties of the Radon transform (and its variants) is the wave front resolution of the singularities of the function under the transformation. This property is underlying many theoretical results in the field, while more recently there have been attempts to design practical computational tools based on the microlocal insights. In particular, in limited data problems, microlocal analysis has proven to provide valuable insights that help facilitate interpretation of images obtained from limited data reconstructions, efficiently design limited data system and even provide ways to improve classical algorithms. In order to exploit microlocal information even further, tools are needed which make this information computationally accessible. Here, we mention the development of directional multiresolution transforms such as directional Wavelets, Contourlets, Curvelets and Shearlets. While those tools have been originally developed in the context of signal and image processing, they allow for exploitation of some more theoretical results and are thus finding more and more applications in inverse problems. In this minisymposium we are going to review some ongoing efforts for development of effective methods for solution of inverse problems informed by microlocal analysis and provide a platform for discussion of new ways how these concepts could be translated into efficient numerical algorithms.

List of speakers

Anuj Abhishek
A Support Theorem for Integral Moments of a Symmetric $m$-Tensor Field
Matthias Ehrhardt
Structured guided Total Variation
Markus Haltmeier
Wavelet methods in photoacoustic tomography
Kim Knudsen
Microlocal stability and instability in Acousto-Electric tomography
Holger Kohr
Total Variation Regularization in variable Lebesgue spaces
Todd Quinto
Artifacts in Arbitrary Limited Data Tomography Problems