  This paper investigates the possibility of improving radio interferometric
images using an algorithm inspired by an optical method known as "lucky
imaging", which would give more weight to the best-calibrated visibilities used
to make a given image. A fundamental relationship between the statistics of
interferometric calibration solution residuals and those of the image-plane
pixels is derived in this paper. This relationship allows us to understand and
describe the statistical properties of the residual image. In this framework,
the noise-map can be described as the Fourier transform of the covariance
between residual visibilities in a new differential Fourier plane. Image-plane
artefacts can be seen as one realisation of the pixel covariance distribution,
which can be estimated from the antenna gain statistics. Based on this
relationship, we propose a means of improving images made with calibrated
visibilities using weighting schemes. This improvement would occur after
calibration, but before imaging - it is thus ideally used between major
iterations of self-calibration loops. Applying the weighting scheme to
simulated data improves the noise level in the final image at negligible
computational cost.
