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