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Surveys of galaxy distances and radial peculiar velocities can be used toreconstruct the large scale structure. Other than systematic errors in thezero-point calibration of the galaxy distances the main source of uncertaintiesof such data are errors on the distance moduli, assumed here to be Gaussian andthus turn into lognormal errors on distances and velocities. Naively treated,it leads to spurious nearby outflow and strong infall at larger distances. Thelognormal bias is corrected here and tested against mock data extracted from a$\Lambda$CDM simulation, designed to statistically follow the groupedCosmicflows-3 (CF3) data. Considering a subsample of data points, all of whichhave the same true distances or same redshifts, the lognormal bias arisesbecause the means of the distributions of observed distances and velocities areskewed off the means of the true distances and velocities. Yet, the medians areinvariant under the lognormal transformation. That invariance allows theGaussianization of the distances and velocities and the removal of thelognormal bias. This Bias Gaussianization correction (BGc) algorithm is testedagainst mock CF3 catalogs. The test consists of a comparison of the BGCestimated with the simulated distances and velocities and of an examination ofthe Wiener filter reconstruction from the BGc data. Indeed, the BGc eliminatesthe lognormal bias. The estimation of Hubble's ($H_{0}$) constant is alsotested. The residual of the BGc estimated $H_{0}$ from the simulated values is$0.6 \pm 0.7 {\rm kms}^{-1}{\rm Mpc}^{-1}$ and is dominated by the cosmicvariance. The BGc correction of the actual CF3 data yields $H_{0} = 75.8 \pm1.1 {\rm kms}^{-1}{\rm Mpc}^{-1}$ .

From Cosmicflows distance moduli to unbiased distances and peculiar velocities