# Three-dimensional Reconstruction of Weak-lensing Mass Maps with a Sparsity Prior. I. Cluster Detection

### Abstract

We propose a novel method to reconstruct high-resolution three-dimensional mass maps using data from photometric weak-lensing surveys. We apply an adaptive LASSO algorithm to perform a sparsity-based reconstruction on the assumption that the underlying cosmic density field is represented by a sum of Navarro–Frenk–White halos. We generate realistic mock galaxy shear catalogs by considering the shear distortions from isolated halos for the configurations matched to the Subaru Hyper Suprime-Cam Survey with its photometric redshift estimates. We show that the adaptive method significantly reduces line-of-sight smearing that is caused by the correlation between the lensing kernels at different redshifts. Lensing clusters with lower mass limits of $10^{14.0}h^{−1}M_\odot$, $10^{14.7}h^{-1}M_\odot$, $10^{15.0}h^{−1}M_\odot$ can be detected with $1.5\sigma$ confidence at the low ($z<0.3$), median ($0.3\le z < 0.6$), and high ($0.6 \le z < 0.85$) redshifts, respectively, with an average false detection rate of $0.022$ deg$^{-2}$. The estimated redshifts of the detected clusters are systematically lower than the true values by $\Delta z \sim 0.03$ for halos at $z \le 0.4$, but the relative redshift bias is below $0.5$% for clusters at $0.4 < z \le 0.85$. The standard deviation of the redshift estimation is $0.092$. Our method enables direct three-dimensional cluster detection with accurate redshift estimates.

Publication
The Astrophysical Journal