Information Field Theory

Information Field Theory Group

Information field theory (IFT) is information theory, the logic of reasoning under uncertainty, applied to fields. A field can be any quantity defined over some space, e.g. the air temperature over Europe, the magnetic field strength in the Milky Way, or the matter density in the Universe. IFT describes how data and knowledge can be used to infer field properties. Mathematically it is a statistical field theory and exploits many of the tools developed for such. Practically, it is a framework for signal processing and image reconstruction.

The IFT research group at MPA

  • develops the conceptual and mathematical framework of IFT
  • derives generic and targeted imaging algorithms within IFT
  • develops the computational tools required for IFT algorithms
  • applies IFT to measurement problems in cosmology, high energy astrophysics, and other areas.


The temperature fluctuations in the cosmic microwave background (CMB) and the cosmic matter distribution in the large-scale structure (LSS) are both tracers of the primordial quantum fluctuations. Those are believed to have happened during the very first moments of the Universe in the inflationary epoch. CMB and LSS are therefore our primary information sources on cosmology. Their detailed studies provide us insight into the history, geometry and composition of the Univserse. IFT permits us to construct optimal methods to analyse and interpret CMB and LSS data, and to image with high fidelity the cosmic structures imprinted in those datasets.

High-Energy Astrophysics

The Universe is permeated by high-energy particles and magnetic fields. Charged particles with nearly the speed of light spiraling around in the magnetic fields, which themselves are bound to the cosmic plasma. The particles and fields are important ingredients of the interstellar and intergalactic media. They transport energy, they push and heat the thermal gas, and they trace violent processes in cosmic plasmas. A number of observational windows in basically all electromagnetic wavebands, ranging from the radio to the gamma ray regime, provide us with direct and indirect vision into the high energy Universe. The IFT group develops special purpose methods to better imagine relativisitc particles, magnetic fields, and even to tomographically reconstruct their distributions within the Milkey Way.  

Other Applications

IFT is applicable to many other areas. The IFT group at MPA has started to work on medical imaging, on numerical methods regarding calculations as an inference problem, on better simulation schemes for partial and stochastic differential equations, and more.

IFT Resources

There exist introductory articles and lecture notes, scientific publication on theory and application of IFT, and a number of commputational tools (NIFTY) and algortihms (D³PO, RESOLVE), which can all be used freely.

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