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We present a Bayesian reconstruction algorithm that infers thethree-dimensional large-scale matter distribution from the weak gravitationallensing effects measured in the image shapes of galaxies. The algorithm isdesigned to also work with non-Gaussian posterior distributions which arise,for example, from a non-Gaussian prior distribution. In this work, we use alognormal prior and compare the reconstruction results to a Gaussian prior in asuite of increasingly realistic tests on mock data. We find that in cases ofhigh noise levels (i.e. for low source galaxy densities and/or high shapemeasurement uncertainties), both normal and lognormal priors lead toreconstructions of comparable quality, but with the lognormal reconstructionbeing prone to mass-sheet degeneracy. In the low-noise regime and on smallscales, the lognormal model produces better reconstructions than the normalmodel: The lognormal model 1) enforces non-negative densities, while negativedensities are present when a normal prior is employed, 2) better traces theextremal values and the skewness of the true underlying distribution, and 3)yields a higher pixel-wise correlation between the reconstruction and the truedensity.

Bayesian weak lensing tomography: Reconstructing the 3D large-scale distribution of matter with a lognormal prior