  We explore a new Bayesian method of detecting galaxies from radio
interferometric data of the faint sky. Working in the Fourier domain, we fit a
single, parameterised galaxy model to simulated visibility data of star-forming
galaxies. The resulting multimodal posterior distribution is then sampled using
a multimodal nested sampling algorithm such as MultiNest. For each galaxy, we
construct parameter estimates for the position, flux, scale-length and
ellipticities from the posterior samples. We first test our approach on
simulated SKA1-MID visibility data of up to 100 galaxies in the field of view,
considering a typical weak lensing survey regime (SNR $\ge 10$) where 98% of
the input galaxies are detected with no spurious source detections. We then
explore the low SNR regime, finding our approach reliable in galaxy detection
and providing in particular high accuracy in positional estimates down to SNR
$\sim 5$. The presented method does not require transformation of visibilities
to the image domain, and requires no prior knowledge of the number of galaxies
in the field of view, thus could become a useful tool for constructing accurate
radio galaxy catalogs in the future.
