3D Reconstruction of the Density Field: An SVD Approach to Weak Lensing Tomography

TL;DR

This paper introduces a novel SVD-based method for 3D mass mapping from gravitational lensing data, offering near-optimal resolution, faster computation, and robust cluster de-blending without prior statistical assumptions.

Contribution

The paper presents a new SVD truncation approach for 3D lensing mass reconstruction that outperforms Wiener filtering in speed and resolution, with minimal assumptions.

Findings

Achieves near-optimal angular resolution in lensing maps.

Reconstructs mass distributions 100-1000 times faster than Wiener filter.

Limited resolution in the redshift direction due to linear, non-parametric methods.

Abstract

We present a new method for constructing three-dimensional mass maps from gravitational lensing shear data. We solve the lensing inversion problem using truncation of singular values (within the context of generalized least squares estimation) without a priori assumptions about the statistical nature of the signal. This singular value framework allows a quantitative comparison between different filtering methods: we evaluate our method beside the previously explored Wiener filter approaches. Our method yields near-optimal angular resolution of the lensing reconstruction and allows cluster sized halos to be de-blended robustly. It allows for mass reconstructions which are 2-3 orders-of-magnitude faster than the Wiener filter approach; in particular, we estimate that an all-sky reconstruction with arcminute resolution could be performed on a time-scale of hours. We find however that linear, non-parametric reconstructions have a fundamental limitation in the resolution achieved in the redshift direction.