We perform lens modelling and source reconstruction of Submillimeter Array (SMA) data for a sample of 12 strongly lensed galaxies selected at 500$mu$m in the Herschel Astrophysical Terahertz Large Area Survey H-ATLAS. A previous analysis of the same dataset used a single S`ersic profile to model the light distribution of each background galaxy. Here we model the source brightness distribution with an adaptive pixel scale scheme, extended to work in the Fourier visibility space of interferometry. We also present new SMA observations for seven other candidate lensed galaxies from the H-ATLAS sample. Our derived lens model parameters are in general consistent with previous findings. However, our estimated magnification factors, ranging from 3 to 10, are lower. The discrepancies are observed in particular where the reconstructed source hints at the presence of multiple knots of emission. We define an effective radius of the reconstructed sources based on the area in the source plane where emission is detected above 5$sigma$. We also fit the reconstructed source surface brightness with an elliptical Gaussian model. We derive a median value $r_{eff},sim 1.77,$kpc and a median Gaussian full width at half maximum $sim1.47,$kpc. After correction for magnification, our sources have intrinsic star formation rates SFR$,sim900-3500,M_{odot}yr^{-1}$, resulting in a median star formation rate surface density $Sigma_{SFR}sim132,M_{odot}$ yr$^{-1}$ kpc$^{-2}$ (or $sim 218,M_{odot}$ yr$^{-1}$ kpc$^{-2}$ for the Gaussian fit). This is consistent with what observed for other star forming galaxies at similar redshifts, and is significantly below the Eddington limit for a radiation pressure regulated starburst.
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