Three-Dimensional Reconstruction of Weak Lensing Mass Maps with a
  Sparsity Prior. I. Cluster Detection
  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 shape catalogues
by considering the shear distortions from isolated halos for the configurations
matched to 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 ($0.3\leq
z< 0.6$) and high ($0.6\leq z< 0.85$) 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 $z\leq 0.4$, but the relative redshift bias is below
$0.5\%$ for clusters at $0.4<z\leq 0.85$. The standard deviation of the
redshift estimation is $0.092$. Our method enables direct three-dimensional
cluster detection with accurate redshift estimates.
