Information field theory
This foundational theory addresses complex inverse problems in fields like cosmology and numerics, offering a systematic approach for researchers in signal processing and data analysis.
The authors tackled the challenge of non-linear image reconstruction and signal analysis by introducing Information Field Theory (IFT) as a Bayesian framework for inference on spatially distributed signals, enabling optimal algorithm construction for complex inverse problems.
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.