Smooth stochastic density field reconstruction

TL;DR

This paper presents a novel method for reconstructing smooth, continuous, and high-order differentiable density fields from discrete point data, improving artifact reduction and faint structure detection.

Contribution

The method enhances Delaunay tessellation-based density estimation by ensemble averaging, reducing artifacts and preserving features in poorly sampled regions.

Findings

Reduces artifacts in density reconstructions

Preserves faint structures in point distributions

Applicable to image denoising and artifact removal

Abstract

We introduce a method for generating a continuous, mass-conserving and high-order differentiable density field from a discrete point distribution such as particles or halos from an N-body simulation or galaxies from a spectroscopic survey. The method consists on generating an ensemble of point realizations by perturbing the original point set following the geometric constraints imposed by the Delaunay tessellation in the vicinity of each point in the set. By computing the mean field of the ensemble we are able to significantly reduce artifacts arising from the Delaunay tessellation in poorly sampled regions while conserving the features in the point distribution. Our implementation is based on the Delaunay Tessellation Field Estimation (DTFE) method, however other tessellation techniques are possible. The method presented here shares the same advantages of the DTFE method such as self-adaptive scale, mass conservation and continuity, while being able to reconstruct even the faintest structures of the point distribution usually dominated by artifacts in Delaunay-based methods. Additionally, we also present preliminary results of an application of this method to image denoising and artifact removal, highlighting the broad applicability of the technique introduced here.