Increasing the Fisher Information Content in the Matter Power Spectrum by Non-linear Wavelet Weiner Filtering

TL;DR

This paper introduces a non-linear wavelet Wiener filtering technique to recover lost information in the matter power spectrum, significantly enhancing Fisher information before the translinear regime.

Contribution

The authors develop a mathematical non-linear Wiener filter in wavelet space to separate Gaussian and non-Gaussian structures, improving information retrieval in large-scale structure data.

Findings

Non-Gaussian power dominates at small scales.

Gaussian component is damped at small scales.

Fisher information increases by a factor of three.

Abstract

We develop a purely mathematical tool to recover some of the information lost in the non-linear collapse of large-scale structure. From a set of 141 simulations of dark matter density fields, we construct a non-linear Weiner filter in order to separate Gaussian and non-Gaussian structure in wavelet space. We find that the non-Gaussian power is dominant at smaller scales, as expected from the theory of structure formation, while the Gaussian counterpart is damped by an order of magnitude on small scales. We find that it is possible to increase the Fisher information by a factor of three before reaching the translinear plateau, an effect comparable to other techniques like the linear reconstruction of the density field.