From the webpage:
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.
IFT is fully Bayesian. How else can infinitely many field degrees of freedom be constrained by finite data?
It can be used without the knowledge of Feynman diagrams. There is a full toolbox of methods.
It reproduces many known well working algorithms. This should be reassuring.
And, there were certainly previous works in a similar spirit. See below for IFT publications and previous works.
Anyhow, in many cases IFT provides novel rigorous ways to extract information from data.
Please, have a look! The specific literature is listed below and more general highlight articles on the right hand side.
Just in case you want to be on the cutting edge of information extraction. 😉
And you might note that Feynman diagrams are graphic representations (maps) of complex mathematical equations.