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We propose a novel method to reconstruct high-resolution three-dimensionalmass maps using data from photometric weak-lensing surveys. We apply anadaptive LASSO algorithm to perform a sparsity-based reconstruction on theassumption that the underlying cosmic density field is represented by a sum ofNavarro-Frenk-White halos. We generate realistic mock galaxy shape cataloguesby considering the shear distortions from isolated halos for the configurationsmatched to Subaru Hyper Suprime-Cam Survey with its photometric redshiftestimates. We show that the adaptive method significantly reduces line-of-sightsmearing that is caused by the correlation between the lensing kernels atdifferent redshifts. Lensing clusters with lower mass limits of $10^{14.0}h^{-1}M_{\odot}$, $10^{14.7} h^{-1}M_{\odot}$, $10^{15.0} h^{-1}M_{\odot}$ canbe detected with 1.5-$\sigma$ confidence at the low ($z<0.3$), median ($0.3\leqz< 0.6$) and high ($0.6\leq z< 0.85$) redshifts, respectively, with an averagefalse detection rate of 0.022 deg$^{-2}$. The estimated redshifts of thedetected 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 theredshift estimation is $0.092$. Our method enables direct three-dimensionalcluster detection with accurate redshift estimates.

Three-Dimensional Reconstruction of Weak Lensing Mass Maps with a Sparsity Prior. I. Cluster Detection