# 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 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 1014.0h−1M⊙, 1014.7h−1M⊙, 1015.0h−1M⊙ can be detected with 1.5-σ confidence at the low (z<0.3), median (0.3≤z<0.6) and high (0.6≤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 Δz∼0.03 for halos at z≤0.4, but the relative redshift bias is below 0.5% for clusters at 0.4<z≤0.85. The standard deviation of the redshift estimation is 0.092. Our method enables direct three-dimensional cluster detection with accurate redshift estimates.