Non-linear image reconstruction and signal analysis deal with complex inverse
problems. To tackle such problems in a systematic way, I present information
field theory (IFT) as a means of Bayesian, data based inference on spatially
distributed signal fields. IFT is a statistical field theory, which permits the
construction of optimal signal recovery algorithms even for non-linear and
non-Gaussian signal inference problems. IFT algorithms exploit spatial
correlations of the signal fields and benefit from techniques developed to
investigate quantum and statistical field theories, such as Feynman diagrams,
re-normalisation calculations, and thermodynamic potentials. The theory can be
used in many areas, and applications in cosmology and numerics are presented.Comment: 8 pages, in-a-nutshell introduction to information field theory (see
http://www.mpa-garching.mpg.de/ift), accepted for the proceedings of MaxEnt
2012, the 32nd International Workshop on Bayesian Inference and Maximum
Entropy Methods in Science and Engineerin
