Information field theory

TL;DR

Information field theory (IFT) provides a Bayesian framework for optimal signal reconstruction in complex, non-linear inverse problems by leveraging statistical field theory techniques, applicable across various scientific fields.

Contribution

This paper introduces IFT as a novel approach combining Bayesian inference with statistical field theory methods for non-linear, non-Gaussian signal reconstruction.

Findings

IFT enables optimal signal recovery in complex inverse problems.

IFT incorporates techniques like Feynman diagrams and renormalization.

Applications demonstrated in cosmology and numerical analysis.

Abstract

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.