Smooth stochastic density field reconstruction

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 haloes 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 artefacts 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 artefacts in Delaunay-based methods.