Astrophysical data analysis with information field theory
Torsten A. Enßlin · AIP conference proceedings · 2014
Abstract. Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), 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. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented. INFORMATION FIELD THEORY Information field theory (IFT) is information theory for fields, describing in mathematical language how information on spatially distributed quantities following some physical laws can optimally be extracted from data. IFT exploits known or inferred correlation structures of the field of interest s (s is regarded as a fuction s = s(x) and as a vector s = (sx)x∈Ω in a function space) over some domain Ω = {x} in order to regularize the otherwise ill-posed inverse problem of determining virtually infinitely many field degrees of freedom from a finite dataset d = (d1,... dn)T = (di)i, n ∈ N. What distinguishes it from many non-parametric inference methods is that an IFT is defined over continuous spaces, and any pixelization of the field used in actual computations must preserve this continuum limit and recover it for infinitely small pixels. A concise introduction into IFT can be found Ref. [1], exhaustive ones in Refs. [2, 3], and the numerical issues of properly discretized fields are addressed in Refs. [4, 5]. Signal field estimation in IFT relies on Bayes theorem that gets recast into a (statistical) field theoretical language: P(s|d) = P(d|s)P(s) P(d) ≡ e